You need to hit it with about 15~20psi for a moment to seat the lid properly. Then do your lea check. The lids on cornies need pressure to properly seal, as the lid lock isn't enough.
As for storage of the others, it seems that the most common recomendation is to use gas to carbonate at serving temps. Since you can't do that in a closet, most would recomend priming and naturally carbing like you would a bottle. You will get a little more settlment in the keg, but it should pour out by the thrid pint.