A:AnswerIt's an adapter for bluetooth, so I don't know it's intended for wifi. I would suggest looking into an adapter specifically for WiFi. For one thing, the transmission speeds are very different. Bluetooth is much slower than WiFi.
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.