The mother will be the woman you see find him when he ends up in Thamasa in one of his dreams.
As for Strago, I think he's more of an adoptive grandfather since the mother died and Shadow left. I don't think he's actually related.
As for the ending (SPOILERS):
Spoiler:
In the SNES version at least, I think he dies. While the others are escaping, he just seems to sit down and act as if he's ready to die now or something.
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