A:AnswerYou can only download apps available for fire tv from the amazon app. So officially yes a limited set of apps.
But, there are websites that describe how to sideloading apps to your Fire TV through the Apps2Fire app available on the Google Play store.
A:AnswerYou can connect to headphones with bluetooth and use that instead of the tv speakers if you want, if that is what you are asking.
I think someone else here had previously asked if they could use this as bluetooth speaker and the answer was nope.
A:AnswerIt doesn't matter in the least which HDMI channel you use.
Do make sure you switch to "last input" or it will start up on Amazon every time you switch it on.