hmm, i dont think i will get to all your questions but i will try.
first i recommend you read up a bit more on the growing. this is not to discourage you or me acting like a dick, its jsut that you have lot of questions that are answered already in guides all over the net. since you are at the beginning its normal to have a lot of questions, but it is a lot easier to get answers if people think you did your homework.
so, an insulin syringe is a normal syringe that is smaller (less capacity, 1ml) and probably has a needle already attached. these are not ideal, as the needle is quite fine and might clog up when injecting.
the idea of the spore print is this. all the spores are on a surface, stuck to it. it is a dry sterile medium that is very good for storage.
to create a spore syringe, you need a normal syringe (~5ml min, 20ml probably is overkill), and several needles. all of these sterile.
in sterile conditions (the glovebox people mention, though it is possible to do without it if one is patient and very meticulous), you scratch off ~0,5 square cm from the print (so you detach the spores using the tip of a sterile needle) into a sterile solution (this can be distilled water, for instance, and will be the ml you want, for instance, 5-10ml). faucet water is not good enough, as it isnt sterile, but you may use water for injections that might be sold in pharmacies. an alternative is to use bottled spring water, if it is sterile (and unopened!). the solution is mixed. this now contains thousands of spores in a watery medium.
using a new needle and the sterile syringe, you suck up the solution.
presto. you now have a spore syringe.
usually people leave the spores in this solution to hydrate for a up to a couple of days, but they can stay like this for a long time too.
alternatively, you could go for a liquid culture first. this means putting the spores into a sterile solution of water+sugars (think preparing a mix of water+honey, then sterilizing it in a jar). the spores get transferred in this solution, and germinate (they will create "fluffy clouds", that you can use later to colonize jars).
the talk about sterility and cleanness is that you want to give only your spores the best shot at growing, not all fungus or bacteria. if you dont, the substrate you have is a hospitable environment for a lot of things to grow, many of which might kill off the fungus.
good luck