Another thing to kept in mind with 4k is the response time and input lag is going to be higher. In my experience 1440p monitors give me a headache gaming, so I'd assume 4k would be more of the same, but that's just my guess.
Yes, same FPS at 1080p!
You're not going to find any good headphones that are wireless in that price range. You'd be better off getting a good pair of wired headphones and if needs be buy an extension cable.
if you're spending that much you should definitely be getting surround sound because you'll get far better quality from five speakers rather than just two. or even just a good pair of turtle beaches with the surround sound software