A:AnswerThis would enable your PC to have a Bluetooth connection, however I recommend verifying with your TV manufacturer that it can be used as an audio source for a PC.
A:AnswerYes. Xbox controller compatibility is native to Windows 10 provided you have that, likely earlier versions as well. Just install and pair in PC settings bluetooth devices, and off you will go. It might lose your pairing with the Xbox itself and you would need to re-pair to use there.