Your questions seem realistic for me so here is my spin. First know that I am NOT a paintball user so factor that in!!
First a small bit of word about the techie talk of gas? CGA 320 is a spec put out by the gas association to help get the fittings more standard, at least in the US. CGA 320 refers to the shape of the fitting that normally ties the regulator to the CO2 tank. That is a place where one would normally use the white washer. Maybe the one you mention?
A picture here?
https://www.google.com/search?q=CGA...=q8iCWPbEJc_AjwP4nq_4AQ#imgrc=rHvmBhKDMeBoHM:
For threads and fittings, there is a general rule for things. If there is a washer, etc. to make the seal, no tape or goo is needed. Compressing the washer does the seal. CGA320 to tank is that type.
If there is no seal like where threads are screwed into threads, pipe dope or tape is often needed. Both work the same so it is often personal choice for which you like.
General rule is that the tape needs to be put on somewhat carefully on small fittings around gas where putting it on wrong can let some get cut off and it winds up in the small passage in something. Bad clog and can be hard to fix.
My method? I hold the fitting that I'm putting tape on, in my left hand as I wrap the tape clockwise on the fitting. What this does is let the tape wrap around so that as it is screwed together the tape is pushed tighter rather than unwrapping. Three wraps is my group's standard but that can be different at times if the fitting is one which is extra tight or one wants it to come tight with the parts in a different alignment. Leave some bare space on the forward end of the male fitting so that the tape doesn't get into the works.
Start with three and if the parts wind up tight but not really aligned the way you want, you can take it apart and add more or less to kind of "fudge" things. Three is good for most cases and just don't feel the need to kill it on small brass fittings. They strip easy!