Well, it was Link's Grandmother in WW, and would hold true for PH... But it would be interesting to see what kind of influence a more involved, deeper sense of family would affect Link's journeys..
Well, I don't know how a deeper sense of family would affect Zelda, because it's always been him going of on his own, or with a helper, and if he had close family that would change it quite a bit. I'm not sure if it would change it in a good way or not.
Well for MC that was his father that he was living with.
No, I'm almost definite that he lives with his Grandfather in MC.
EDIT: Actually, I just checked and, in MC, when you get the Smith's sword it says "you got the Smith's sword! This sturdy sword was forged by your Grandfather".