Responses
(All of this are theories) For the father ,yes he is.. Different mother or an illegitimate, adopted by the family. The old man might be as you said close to the crown. My theory is that he might be a the lord of the magic tower or somesort. Since he knew a lot of nobility and able to talk to them.
The magic tower theory makes more sense to me
Prediction:
That grandpa is a fallen/exiled hero who has trained the royal family, possibly a high ranking noble himself. But since he is not avoiding travel or anything, I think he is a retired commander that has lost his family and sense of self. So he is trying to redeem himself by doing good deeds. ╮(￣▽￣)╭ medium confidence but he doesn't seem like a hidden villain, just (plain) suspicious
Tyr's father is that missing nobleman and he is either the current hero on an undercover mission or family black sheep since it's full of prodigies ┗( T﹏T )┛ This is a weak one. Need more info to properly flesh it out