Okay, i've extracted dxm a few times, and some other things.
the first time I tried to extract dxm with ammonia it didn't work cuz i used CLEAR AMMONIA from walmart but it really has surfactants. The surfactants will cause an emulsion that you cannot seperate. I use janitorial strength ammonia from ace hardware, it has no surfactants is just 10% ammonia which does not foam at all when shaken. I have used this ammonia to extract dxm many times, I have kept it as a freebase as well as making the HCL salt of dxm. I have gotten freebase snow white kindof a waxy powder...the hcl was usually offwhite crystals but can burn easily and turn yellowish if you use the oven to evaporate the HCL/water.
you could use NaOH for your base (its certainly strong enough) as long as the syrup doesn't have guafenesin...i have heard sodium carbonate works too but cannot say with certainty that carbonate works. I know ammonia works from personal experience, and i know NaOH would work.
As for you questions:
1. i don't think it has to be that complicated with molar equations and shit...i'm too lazy for that, you just need a sufficiently high ph to cause the dxm to precipiated out as the freebase which you will see as the solution getting cloudy...and stay that way. I think a ph of 9 or more is suffient for dxm
2. excess base will stay in the aqeuous layer as it is not soluble in your nonpolar solvent. doing subsequent water washes on your organic layer with clean water will remove any leftover caustic soda that might have made it into your organic layer.
3. I honestly cannot say for sure..I wouldn't use diethyl ether, it's more expensive, and more dangerous...especially when you are trying to evaporate it. I would use naptha, or colemans fuel (basically naptha with blue dye), toluene or xylene...i've used naptha to great success and it seperates perfectly. Starter fluid is not pure diethyl ether...its usually more heptane than ether anyway. If you use ether just be careful and if you're worried about the slight water solublility...do several pulls on your aqueous phase and combine them...anything leftover would be diluted out if that makes any sense.
4. You just need enough organic solvent to make about a half inch layer or so...its not that critical with the amount i've never used any exact measurements of the solvent..dxm freebase is quite soluble in nonpolar organic solvents so you won't need as much solvent as syrup/aqueous layer.
5. Yes you can do multiple pulls with your organic solvent on your aqeous phase and continue to pull dex out.
Once you seperate your organic layer you can wash it with clean water (preferably distilled but i use tap water) and seperate discarding the water. You can do this one or more times. DXM as freebase is water insoluble so the water will just pull out any water soluble junk. You might not care how clean you get it...thats up to you but if you want a clean white dxm extract you should wash your organic layer with water several times.
You can stop here and evaporate your organic solvent and be left with hopefully white crystals of waxy dxm freebase. DXM freebase still tastes bad but not as bad as the salt because the freebase isn't water soluble.
If you wanna go further and make the salt you could either make an acid pump and gas it out with hcl gas, or make a dilute aqueous solution of HCL and shake this together with the organic solvent, then seperate...this time keeping the aqueous (bottom) layer. If you use aqeuous hcl you can wash this with some clean nonpolar solvent to further remove junk and seperate again, discarding the organic solvent. Then you must evaporate the water/acid. From my personal experience you want to use as little acid as possible to salt out your dxm into the aqueous layer (i always use like a capful which is way too much) because when you evaporate it in the oven or microwave or whatever it will release white HCL fumes which will make it impossible to be in the vicinity unless you have good ventilation. I'm sure you could use alot of other acids but the thing about hcl is if you use too much it escapes as a gas when the water evaporates so you don't have to do a lot of math to make sure you don't end up with excess acid in the product.
DXM HCl hits very hard but is the nastiest, foulest tasting shit i have ever tasted. You think zicam tastes like shit...well this shit makes that seem like nothing. DO NOT do it any other way than oral or you will regret it...the crystals look like you could use several other routes of administration with them but you don't want to do that.