There is a lot to unpack here and I won't claim to being a complete expert. I also may have to break it up a bit since we are experiencing some serious freaking storms and my power keeps shorting out. So if this ends up looking like paste in job, its because it is.
1. It depends honestly on what flavor of communism, socialism, or anarchy you end up with. Anarchists, who I respect immensely, believe that you can do this almost purely through mutual cooperation but I'm realistic enough to know that at best, there is going to be some sort of democratically chose set of standards. Understand too that "State" in the communist critique relies heavily, heavily on stratification and hierarchy. Contrarily, the communist version instead replaces stratification and hierarchy with absolute democracy forming what Engels referred to as the "dictatorship of the proletariat." I know that seems like "six of one, half dozen of the other" but with the abolishment of the class system and lacking a set of classes available to exploit, a whole apparatus of capitalist state control no longer exists.
So the setting of standards then would likely be those enforcing those concepts of democracy and basic rights as a primary system much in the same way that the Anti-Federalists in America assumed that the Constitution would be enough because "all other rights are inherent."
So how is this managed? Well, syndicalists would pursue charters determining their own labor groupings so prices set under The Union of Plumbers and the Union of Clinicians would set prices under their own and disagreements that are considered exploitative or troubling would be hashed out not just between those two but all syndicates. I would imagine the closest thing to this is a parliament of syndicates of sorts but I doubt they'd use that term. Anarchists would likely choose the same thing but without the syndicates (because they view syndicalists as hierarchical) but participation would be much more local (neighborhoods, sectors, cities, regions, etc) again democratically but region segmented (as a guess). SocDems would likely function very much in the same way that we do know as they are the closest to capitalists without the capitalist system.
And yes, the big state is a problem. Vanguard parties are power concentrations as they were in Russia, China, and even Cuba. A communist scholar would probably lampoon all of those as and call them state welfare capitalists with "communist stickers" because with vanguardists, the proletariat are quickly forgotten for their "own good." Realistically the biggest impediment to the proletariat will always be keeping a watchful eye.
2. Yes, market commerce will always be a thing and yes, some people will have more labor value than others. The difference here is: 1. A laborer of any job will be getting their full value of labor (you won't be paying out a percentage of your pay to your boss who does not do the work). 2. Jobs won't be locked behind education levels that require massive education systems that benefit those who start from a hereditary, economic, or geographical advantage. 3. With more free time, needs met, and buy in (due to seeking jobs you want rather than what you need to live) to the jobs, people can pursue those career fields that they enoy. 4. Jobs won't be subject to the fluctuation of need that isn't democratically controlled (jobs picked as artifical winners in the current economy heavily favor industries that are often incredible exploitable like capital, military, and energy)
3. As I said in 1. that depends on the system. And there will still be a market, just not as its currently controlled.
4. The simplest answer is because the current set of desires outside of those few people who can truly have anything their heart desires, the vast majority of us do not seek actualization but rather the basic set of protection for their lives and their family. We are worried constantly to maximize our own profitability rather than our own personal values so that we can constantly upgrade. But that drive to upgrade also creates its own cycle by which we seek less of self-actualization and more convenience and quick entertainment. Everything in our lives have been commodified, even our suffering. Marx called this the alienation of the worker from their Gattungswesen (species-esscense) and alienation from other workers.
5. This is honestly the most complex question due to a lot of theory on labor value. The biggest impediment to these would be that our current concept of money as a store of value would change. The most workable real world example comes from the Cincinnati Time Store where goods were purchased with labor vouchers. Labor vouchers, which in some ways acted like money as an exchange, rather than a store of value, were promises of participation to do certain works. Since those are valued by job and skill, the exchange of value is obviously going to be different. Again, example, you may be able to purchase a car with 1,000 labor units of from me as a carpenter but it may take only 100 labor units from me in my capacity as an Operational consultant. Using a labor value system means that you can't "make money off of money" which really makes the issue of heredity disappear. Value has to be stored in produced goods, raw goods, or people. The same sort of applies to nepotism because again, labor value has to be earned. Yes, there may still be some questions of nepotism and even issues of exploitation but with a system where workers are insulated to a vast degree by their own rights, who would realistically give someone more of themselves just because of who their parents are.
Thank you for taking the time and effort to write such a long detailed response to flesh out your ideas, it's posts like this which enable genuine intellectually stimulating debate.
1.
For the purpose of this discussion I'm mostly interested in discussion of a socialist system rather than communism or anarchism, simply because socialist states have existed, some still exist, and this can be observed, whereas communism and anarchism remain entirely hypothetical.
In theory what you say about abolishing hierarchy sounds nice, but it has simply not been the reality in any socialist state. You still get some "privileged few" hogging the resources at the top, except instead of it being business owners it becomes government officials instead. This seems pretty much inevitable unless you were to have a true anarchist society, but you have acknowledged, this is a pipe dream.
The reason you can't get rid of hierarchy is because it is not a social construct but rather is an innate part of human nature. Humans have an innate drive to gain power. Some philosophers even put this above the very need for survival, and instead suggest the need to survive is merely an extension of the need for power. More scientifically, we know that human serotonin levels increase as we move up in social status, regardless of if money is involved or not. So regardless of how you set up the economic system of the society, there will always be a hierarchy of power. And those in power always end up with more resources than the peasants.
It seems to me then that the main variable you can control is who gets a shot at gaining power in society. A socialist system means only a small group of politicians, bureaucrats, and government officials have all the power. In a capitalist system there are opportunities for hypothetically anyone to acquire a level of power, e.g. by being promoted to management, which your vision of society excludes (and I will talk about this in more depth in a minute).
You address this by talking about a democratic system. But your new model for democracy only works if you can abolish the class system entirely. However you also propose that people who do more work get more resources. So how would there not be a class system? If a doctor has more resources than a shopkeeper, how is he not of a higher class?
Finally the matter of a large state. We are in agreement that anarchy is not feasible as a political system, a large state becomes a necessity, and that this is a problem. So not much for us to debate here as we agree on the main points. I merely want to point out that a large state seeking to control more of peoples' lives leads to a higher level of authoritarianism, so therefore socialism and authoritarianism go hand-in-hand. The average plutocrat can have a watchful eye all he wants, but a watchful eye does not stand much of a fighting chance against secret police and gulags. If anything the watchful eye becomes a tool of the state. Stalin and Mao both famously enforced policies of informing on your neighbour.
In short: I believe socialism simply transfers more power away from the people and to the state. And I do not believe the state should ever be trusted.
2.
Interesting that there would still be a marketplace. I assume this marketplace would be controlled heavily by the state in place of bosses, since you dismiss them as "doing no work"?
For one thing I recommend anyone who genuinely believes that bosses don't do any work to try being a CEO or even an upper level manager for a day and then tell me there is no work being done. The reason those jobs are so highly paid is that they require stressful work and very long hours. People in such positions become burnt out from it. They're certainly not just lazing around doing nothing all day while money pours in.
In regards to middle management there are some valid criticisms to be made where ineffective lazy managers can coast along, but the ones making the real money, the top level managers, they are not the same breed at all.
As for how you propose jobs be allocated: is this not already democratic? And does the state controlling it not in fact make it less democratic?
For example if I set up a business selling sand, and no one wanted to pay for sand, I would go out of business. I'd lose money, go into debt, and have to shut down. This is a result of the market demand - the people don't want to buy sand so I can't make money selling it. I need to sell something with consumer demand to be successful.
But if the state set up a business selling sand, and no one wanted to pay for sand, they could keep on employing people to figure out why no one wanted to buy sand, they could spend money on marketing sand in an attempt to get more people interested, they could provide incentives for people to buy more sand, and all the while still lose money and just pour more tax revenue into this venture. It wouldn't matter how unsuccessful this venture was because the state could fund its bloated corpse forever.
This is why in the real world state run businesses are simply inefficient. For that exact reason. Governments today hire so many bureaucrats who sit around doing nothing of any value or meaning. If a private company hired all those bureaucrats they would either be pressured by shareholders to fix that problem or they'd eventually lose too much money and go out of business. The market forces efficiency, as well as forcing businesses to market what consumers want.
As for people having jobs they enjoy... the reason this can't always be the case now is a result of the above. Often the dream jobs a lot of people want to do simply are not in enough demand for everyone to do them. Example a lot of people wanna be rock stars, but there's not enough demand for all those millions of people to actually do so. I don't believe even a strictly controlled state run economy could fix this fundamental mismatch in supply and demand. It could attempt to ignore it and pay people for doing nothing of any use anyway... but you just criticised capitalism for doing the same thing, and at least private companies aren't using public money to do it!
3. Addressed above.
4.
What you are talking about here is not necessarily a flaw in capitalism itself but rather the consumerist culture we live in today. You won't get any argument from me in defence of consumerism, I agree it's a bad thing. But it's also a pretty recent thing. The global economy has largely facilitated it by using cheap labour pools in countries like China. "Fast fashion" is a good example. Being able to walk into Primark and buy bags of new clothes for next to nothing is an extremely recent development. This of course creates other issues too: environmental problems, labour exploitation, etc as well as a culture of throwing things away quickly to always buy the next thing.
I'm honestly not sure what effective solution we could have for this, since globalisation is simply a reality now and you can't put the genie back in the bottle, but I certainly agree it's a problem. Personally I like to buy high quality products that are long-lasting. As the old saying goes "buy cheap, buy twice." If I buy an Apple laptop for £1000 it'll last me much longer than an Acer laptop for £100. If I buy designer clothes made in Italy they will last me much longer than a something from a budget outlet that'll fall apart within a year and was made in a Bangladeshi sweatshop. This means I don't need to keep buying new things all the time because I'm not buying throwaway items.
Of course not everyone can afford luxury goods but there's plenty of middle ground between cheap disposable goods and luxury goods as well. The mid-range level is usually affordable by most.
5.
In this case people will use their "labour vouchers" to buy stores of value, such as gold or even cryptocurrency, and keep those as investments instead of money.
I also have to again bring up to the point that to enforce the value of a good depending on the seller rather than the good itself, you would need state intervention, and somehow the state would need to calculate the value of every item on the planet and link it to the value of every occupation on the planet and then decide who pays what for everything. This is just mind bogglingly impossible to do on a large scale.
The real world example you gave, Cincinnati Time Store, differs from your ideal for two main reasons. One, it was a single store that ran for just a few years - implementing such things on a nationwide scale is of course a much bigger task. Two, it is not based on the idea that you should have to pay more or less based on your job, but rather the cost of goods should be based on the labour going into making it. So whether the buyer is a carpenter or operational manager, the cost of the good is the same, and that cost is based on the labour time of who produced the car. How this would work in the secondary (used) market I don't know, as it's an experimental idea to this day.
The idea itself is not as radical as you may think, since quite obviously the cost of labour is the biggest influence in a value of a good in the capitalist market already. That's why all the manufacturing is done in China. Cheap labour pools. And the more time it takes to make something, the more labour you need. Which is why intricate, handmade, bespoke goods cost so much more than mass-produced goods. A handmade Swiss watch costs more than a fake from China because of the labour costs involved in producing it.