I cut a hole in the ceiling of my closet to vent the heat. The proper tool for this is a keyhole saw. They are not expensive and any home improvement store will have them. Keep the part you cut out and you can use it to plug the hole when you move. Even a half-ass patch job likely won't be noticed in the ceiling of a closet during your move out inspection. If you're really worried about it buy a book on drywall.

It is not healthy for the attic to vent heat into it, but if it is an apartment you don't necessarily have to worry. (Unless the smell is going into your neighbors apt.)

Ideally you want to pull the air through a carbon filter and vent directly out to the roof. This is how bathroom and some kitchen fans are vented. If you can get into the attic you'll see flexible tubes going from the vent fans to the roof. You can find all kinds of adapters and tubing at home improvement stores.

Good luck growing your broccoli