Am I supposed to keep the compressed files of the games I download, or can I delete them to free up space?

I usually zip my game files after certain levels of modding and upload them to my gdrive.

That's basically up to you. Normally when you unpacked a zip file you can keep them for your own personal archive, or if things go wrong with the unpacked version that you still have the original zip. If you do not care about such things, you can  delete the zip files, the game will work without them. 

Depends. If you are not running out of space, keep the latest version of your favorite games. Itch is not a future proof cloud storage. Developers can chose to remove their games any time.