A super simplified damage formula is BaseAtk*CharacterAtk*ElementalAtk.Yes. Yes. yes.Assault is CharacterAtk, and each skill level is 0.5% more damage. Relic weapons are ElementalAtk, and each skill level is 1% more damage.
All damage is boosted - however, please note that Abilities have damage caps. If your Abilities aren't hitting harder, then you're probably at the cap of that specific Ability.Each +1 is +3 Atk and +1 HP. Yes, you can put them on Kamihime as well, but you never want to - it's much better to put them on weapons since that way, EVERYONE in your team gets that very same +3 Atk and +1 HP, not just that one Hime.