You cannot. Touch Mode is not available with Apple TV.
This is a bug specific to the game when played on Apple TV. To avoid it, make sure all guitars are connected before the game begins. Do not try to connect a guitar controller to the game while the game is playing.
You cannot. The Game Center App does not currently support Apple TV and Achievements are currently not available.
No. Rival Challenges are unavailable on for iOS and tvOS on Apple TV versions of Guitar Hero Live.
This can occur on operating systems older than version 8.1.2. Update the operating system to resolve the issue.