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For instance, does any know how to calculate the number of hit points Taka delivers using the three possible attacks(melee, Kaiten, and X-Retsu)? How does that change with +1 crystal power?

I don't actually know what you mean "the number of hit point", do you mean the Damage of skills and relationship with crystal power?

You can see the basic damage in Hero Page, and Kaiten have 120% crystal ratio, that's mean if you mastered Kaiten, the damage is 410 (Lv5 Kaiten damage) + 120% Crystal Power, formula can be suit to X-Retsu.

But Attack don't gain any extra damage by Crystal Power, unless you buy Alternating Current.

Crismisis is correct. Abilities have base damage that benefits from a crystal or weapon damage boost depending on ratios. If I'm not wrong, it should look like this:

A little background- crystal damage refers to damage from abilities while weapon damage refers to damage from basic auto-attacks. Crystal damage is boosted by crystal power and weapon damage is boosted by weapon power.

(Crystal Power * Crystal Ratio) + Base Damage = Total Ability Damage (in crystal damage)

Kaiten:
(100 crystal power * .2) + 410 = 460 crystal damage
X-Retsu:
(100 CP * 1.7) + 730 = 900 crystal damage

I believe Weapon Power is just added to your base damage.
Taka's autoattack at level 12:
100 Weapon Power + 125 = 225 weapon dmg

Most abilities do not benefit from weapon power, however Krul's Dead Man's Rush and Joule's Thunder Strike do have a weapon ratio, so they do have a weapon damage boost that is independent from the crystal damage of the ability.

It is important to note that an ability's damage (or hitpoints taken) is normally mitigated by shield. I'm not sure about this one, but defensive stats are calculated as such:

500 Weapon Power / ((100 armor / 100) + 1) = 250 true damage
500 WP / (1 + 100%) = 250

SO for every 1 point of armor you have, you become 1% more durable to weapon damage. This means half the damage at 100 armor and a third of the damage at 200 armor.
I wouldn't be surprised if shield is similarly calculated. Shield mitigates crystal damage.