How do I fix a hole/gap between my shower tile and the dry wall next to it?
Take a paint stir stick from a home improvement center, break it into pieces that will fit behind the patch hole, and pop in a screw to hold it in place, on the side away from the tile. It doesn't have to be rock solid, it's purpose is to keep the drywall patch in place long enough for the  compound to dry. Once the patch is in place (liberally buttered with compound) and dry, you can remove the screw holding the stick in place- the stick may drop off into the wall, but that's no great problem. Patch the screw hole, and you're set.