(1) You just need a good Graphics card and a large HDD if you want to play latest games.
I really do not think you need to change your PC now even you are studying computer science. If you have deep pocket, it is another matter of course.
(2) You need to change Motherboard as well.
(3) DIY, even your degree course is software based, but it would be good for you if you learn softthing about hardware as well. I seriouly suggest you to acquire more hardware knowledge.