Depends on the state you live in. I gave temporary guardianship to my mom for purpose of school for my oldest daughter and I didn't have the fathers permission. I am the custodial parent therefore I make the decisions. I don't believe you could give permanent guardianship without him though.
No,
He has to know and certainly must know if he is paying child support and perhaps he wants his child if you plan to give up guardianship to someone else it is not fair to not inform him nor is it legal......the best to you