Yes. Any downloaded game from Xbox Live can be moved to USB via Settings → Storage.
No. Even if you install the game to the USB, you must insert the disc every time you play. This prevents piracy. If you want to play disc-free, you would need to purchase the digital version from the Xbox Marketplace. install games xbox 360 usb best
Pro Tip for Multi-Disc Games (e.g., Lost Odyssey, Mass Effect 2): Install Disc 1 on the USB. When the game asks for Disc 2, press the Xbox Guide button, go to "Game Details," and install Disc 2 to the same USB drive. The game will switch automatically. press the Xbox Guide button