Now my Zelda knowledge isn't really the best at midnight, but I think the only time we've ever actually seen one is in ALTTP which would be his uncle.
Although there have been quite a few mentions of actual parents like in OoT. We probably haven't met them I would think due to the James Bond...
Nah. He didn't have to be injured. I mean he probably did die, but Link had the Triforce, and did wish for everything to be back to normal. So I do believe he died, but was brought back to life.