1.In each category, Normal atk, Crit, Multiatk, SkillAtk, C.A dmg. How and what calculation are made?

Normal attack: Base ATK * Weapon Skill Modifier * Elemental Modifier * Character Skill Modifier

Crit: Normal Attack * Crit Modifier. There are two separate crit checks (one for weapons and one for characters with their own crit mechanism)

MultiAttack: Normal Attack x2 or x3. RNG is applied first for TA, if the character fails to TA then it will either DA or attack once.

SkillAtk, : Normal attack * Skill multiplier. Each skill has its unique modifier and cap

CA: Normal Attack * CA modifier. SSR characters/weapons have a modifier of 5 or 4.5 whereas SR and R are rated lower.

2.How many character can "Raise" that damage bar? Please provide a name you can come up with :3

You mean the damage cap right? On top of my head: Ferry (team), Yuel, Izmir and the new SSR trial character (yeah it's Stan)

I can't link it now, but one of Darchrow's guides on xiei.moe explains damage calculation in more detail.