Yes, it is possible using this type of transmitter: Hama Bluetooth Audio Transmitter/Receiver (Transmitter & Receiver)
But this is not recommended, because with Bluetooth you may have a latency between sound and picture, which can be unpleasant when watching a movie.
Unfortunately, I can't answer that. I have connected it to the PC and it works great for teams, Skype and telephony via PC. Of course, I can also listen to music, but it's not a big hit. That's not what the device was designed for. I am fully satisfied, my expectations have been met.