Game disc save

It'll save to whatever storage device you have. If you're wanting to save to the cloud, you would need to enable cloud saves. https://support.xbox.com/en-US/help/games-apps/game-setup-and-play/cloud-save-games-xbox-360

Your game saves will not be effected by installing / uninstalling games discs.

Whatever your level was when the game was saved last is what it will be regardless of the disc being installed or not.

Saves are not stored on the disc. So if you let someone else use the disc, they can play the game on their own save. It won't have any affect on the first person's save.

Load the disc game into your hard drive. That way, the disc only spins at game start. Saves your discs.

Yes, because the saved game is saved to your xbox, not the disc.