So many questions in so few words!
- A 22 ounce CO2 cylinder holds ~12 cubic feet of CO2 at STP.
- 3 gallons of beer carbed to the typical 2.5 volumes of CO2 will consume ~1 cubic foot of CO2
- dispensing a 3 gallon keg will consume ~.4 cubic feet of CO2
So you should get a few 3 gallon kegs out of a single cylinder.
As for carbonating at warm-ish temperatures: take a look at
our favorite carbonation table. If you wanted to carb up your 3 gallon keg o' brew to a typical 2.5 volumes of CO2 at 65°F, you'd set your CO2 regulator for 28-29psi, and leave it alone for a couple of weeks to fully carbonate. If you need to carbonate at a temperature outside of the table's scope, you can use this
force carbonation calculator instead.
When you put that same keg in the fridge and chill it down to, say, 38°F, you would set the regulator to 11 psi, which would maintain the same ~2.5 volumes of CO2 carbonation level. You could do that anytime - even in the middle of force carbonation - and still end up with properly carbed beer. It's all about coordinating CO2 pressure with beer temperature.
Finally, you'll then need to tune your dispensing system to handle that ~11 psi (preferably, aim for a bit higher to give your system some margin). "Tuning", in this case, pretty much means using beer line with the appropriate inside diameter (typically 3/16") with long enough runs to keep the CO2 in the beer from bursting out of solution and causing massive foamy pours. For that, you can use
my favorite line length calculator, which will likely recommend you use 10 foot or longer runs.
That should give you plenty to consider...
Cheers!