IF you could get a good enough seal on the threaded part of the lid, and you could fully bung up the airlock hole, then I reckon you would blow up the fermentor. If by carboy, you mean one of those big glass jobbies, you would blow the bung out for sure. Either way, you will not end up priming your beer.
However, if you put the beer into a keg (stainless steel, soda type or equal) then sealed it up, you would not blw the keg up, and you would naturally carbonate the whole bach in one hit.
Not necessarily - even at low temps there will be some yeast activity. It might take an awful long time but fermentation would continue at a slow rate. I have yeast starters in Grolsch bottles in my fridge and every so often I quickly (and cleanly ) open them to release the pressure - even on ones that in theory have already stopped fermenting.