A:AnswerYes you can use your wifi for that you will need to have your password at hand when ask you to input the neccessary info.
And yes, has a port for headphones. If the mouse use a USB port then, yes you can plug it in.
A:AnswerI can go long periods using my graphic design program on it and it's never heated up. Running something like games though, I don't know if it would or not. For just lighter stuff it has no problem.