1. That's more or less the case, yes.

2. So, the damage you deal. Natural questions since the game does jack to explain anything about this.
For the most part, damage calculation centers around calculating your normal attack damage; that is, the damage of one regular hit. Ability damage is derived from normal attack damage. Burst damage is derived from normal attack damage. Eidolon summon damage is... so insignificant that nobody ever bothered to figure that out.

Fundamentally, normal attack damage is your base atk multiplied by a bunch of other stuff.
The current version of the forumula is:
Base atk * (1 + sum of Character atk stuff) * (1 + sum of Element stuff) * (1 + sum of Vigor type stuff) * (1 + sum of Special type stuff) * (1 + Crit stuff) * (1 + sum of you_getting_atk_debuffed) * (1 + union guardian buff) * (1 + Other_Buffs) / {enemy_defense * (1 + sum of enemy defense buffs and debuffs)}

Generally speaking, things that just say 'attack up' or something like fall under Character atk.
Elemental advantage/disadvantage goes into Element
Other_Buffs is basically a miscellaneous catch all until things get sorted out later. For now, it's things like berserk and the extra damage against stunned/raging enemies stuff.
The vast majority of enemies have 10 defense.

Once you figure out roughly how strong a single normal hit is, ability and burst are simple.

Ability damage is fundamentally normal attack damage * multiplier * number of hits.
Where do ability damage buffs go? They just directly add onto the multiplier. Since they go there, they really benefit a lot from a high number of hits, but are really bad when your abilities only add up to a few hits.

Burst damage is fundamentally {normal attack damage * (multiplier + burst damage buffs) + small_constant} / hits} * hits
Multiplier and the small_constant are based on rarity and whether or not you got it limit broken to 3*
The dividing and multiplying by hits is largely cosmetic for the most part, although apparently later changes to how crits work make that relevant?