Can you install torrented games to Xbox 360 Harddrive?

Not that way. Your 360 has to be modded to read pirated games which means you can't play on Xbox Live. You need to copy a legal copy of the game onto your hard drive not a pirated file. You can do this by renting or borrowing the game. Install it to the hard drive and as long as your copy can be read a bit at startup to verify it, it will then play from the hard drive.