Moff VERY low damage, needs a re-work? Is he for defense only?

The omegas on his basic and first special are required for him to be the most useful.

Regarding Executrix, everything you do to Tarkin affects his capital ship except mod abilities. So that means increasing his level, abilities, gear, and stars, and ensuring all his mods are 5* and fully upgraded will all increase the power of Executrix. I believe the ship gets boosted according to power increase, so the things that give the most power increase to Tarkin would affect Executrix the most.