He would have a hard time making use of the Archmage power to ignore a Bane's immunities, because he often won't be making a check against a bane based on his Charisma or Intelligence where immunity would matter.
He could still utilize the bonus to his Charisma checks and replacement of his highest die with a d20 in other situations, like recharge checks and checks to acquire cards. And he'd be able to use the power to examine a deck.
Mythic Marshall seems well suited to Balazar.
You are right. When Balazar uses Padrig's power to enhance his combat check, Balazar is making a Strength check, not a Charisma check. As an Archmage he couldn't add his mythic charges to this check, nor change any dice to d20s.