Howdy, Belter.
Gear's spent before a roll, Grit's spend after. Them's the breaks. Now I'm not there to keep you honest, so if you want to give it another go with Gear, sayin' that you meant to do it the whole time I'm not going to come and smack the die out of your hand. But the intent is that you're spending Gear when you think to yourself, "Man, I really can't fail this one. Better dig in the toolbelt for an edge..."
As to the second, no amount of sheer grit and determination's going to overcome your need to keep breathing. Gas does its own thing and is unaffected by any other mechanics aside from certain kinds of Bad News.
Entering your Airlock does indeed prompt a Gas check, like transiting all modules. You can stay in there and hold the door for your buddy without checking it, but the decompression/pressurization cycle is long enough to make waiting on the Belter's Prybar hatch have you checking your wristcomp and maybe saying "C'mon, c'mon, c'mon..." Movement around a Bird can be counted on to have one constant. Token moves? Check gas.
Hope that gets you sorted, Belter.
Chariot, out.