I don't think that Rusl could be Link's father, because of things that are said in the game. For example, when the pregnant woman (forgot her name) gives Link the fishing rod she says something to the effect of "Colin made it with his father" - if Rusl was Link's father, it would have made more sense (and been more correct) to say "...with *your* father."
My assumption always was that Rusl was either Link's uncle, or had been been very close friends with Link's parents before they ... died or whatever. It's possible that Rusl helped raise Link, and depending on how old Link was when his parents "left," Link may have lived with Rusl for a while. However, since Link has his own home, I suppose that was the home his parents lived in, and he was probably old enough to live independently when they left, with just some guidance and help from Rusl.
Colin would probably have looked up to Link even if Rusl hadn't been Link's mentor (all the other kids do, after all), but it does seem like that mentor relationship has made Link a bit like a part of the family. (On the other hand, I always feel like Colin's mother doesn't know Link very well - she seems very formal with him.)
As for Rusl being a previous incarnation of Link... I could see that being possible. I doubt that we'd ever get a game about his story, but he definitely seems like he's got the skillz. Whether he has been a Link or not, he's definitely got "hero cred."
One thing I thought of that might debunk this part of the theory is the existence of the Hero's Shade. My impression was that he was the Link immediately preceding TP's Link, who had died without passing on his knowledge. (That would be hard to support though, since there's no evidence of any of the Link's taking on an apprentice.) If that were the case, though, if any other Link had been around since the Shade's death, couldn't he have just taught that one instead?
I would definitely love to have more backstory for TP - I'd say it's probably the game that I most want to have more of the story of.