A:AnswerYes, this bluetooth adapter allows Bluetooth devices to connect to a pc. PS4 controller does support Bluetooth. You need to pair the controller with the adapter. Just google how to connect a PS4 controller to a PC using Bluetooth and follow their instructions. You should be playing wirelessly right away.
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.