Does the instalation of Cyberwear requirer a special feat or can any doc try it?
Any one can do it. but if you want to survive, best to get a Doc with the Medical Skil and the Surgery feat
What happens if a doc fails the check? do u lose hit points?
Well, the implant does not take and what happens next really depends upon what he was getting replaced. Say he was getting a cyber eye, there would be some hit point damage, but the character should really be more worried he is now missing an eye.
Generally all surgery on PC's should work, unless there is a specific GM reason for it not to. The DC's should only really be worried about when the players are doing the surgery. Then it is really up to the GM what happens if they fail. Especially with the relatives/firends of the one on the table if it went really badly.
What happens if you have a cyberlimb and you lose it...Do u gain your self points? If not do u lose more when u get a new cyberlimb? I say yes because its a constent wear on your humanity but my players say otherwise.
You do not regain self points until you have had some form of therapy. You would not regain the self points from losing a cyberarm (I would be tempted to add to the loss) and you certainly lose some more when you go under the knife to get another one added. I would probably half the loss the second time as most of the surgery has been done.