Advantages of a primary, dominant-element team
By sanahtlig

KamiPro has multiple mechanics that encourage focusing on a core team of same-element characters. Assault skill and related effects give large character attack bonuses to characters of the matching element, and these bonuses are multiplied by the elemental attack bonuses granted by the more valuable eidolons, which are typically mono- or dual-element. These bonuses are very important to damage output, and having fewer than 4 same-element characters in a team of 5 generally isn’t recommended except in special circumstances.

While leveraging elemental-advantage can be effective in early- and mid-game, focusing resources on a single element is typically the quickest way to progress into Ultimate and Ragnarok content. That means prioritizing that element for weapon farming (including from Disasters), farming of 1-2 strong fully limit breaked primary eidolons, weapon leveling, and weapon skill leveling. Weapon skill leveling (mainly assault skill) is the main bottleneck, as skill fodder is fairly scarce and it takes several months to max the skill levels of an entire grid.

Another advantage of focusing on a single element is that you’ll be enhancing your best team and using it for most content. A well-balanced team combines adequate healing, a variety of essential debuffs, and strong spike damage, and players typically won’t have the necessary variety of kamihime to build such a team for every element.

Gacha
By sanahtlig
See the Gatcha Calculator in Sanahtlig’s Kamihime Project Toolbox for a rate analysis.

Cashing priority
Miracle ticket* >> SSR kamihime ticket >> Premium Gatcha

For obtaining a specific SSR kamihime:
Miracle ticket >> SSR kamihime ticket = 19x Premium Gatcha (5x appearance bonus) = 95x Premium Gatcha (no appearance bonus)

* Not yet available
Appearance bonus
The Appearance bonus (Rate up) for newly-added characters increases the chance of pulling the newly-introduced kamihime, out of the pool of all kamihime for that rarity tier, by 5x. This will eventually be raised to 15x. The bonus for eidolons is 2.5x.

Stat buffs and debuffs
Stat buffs and debuffs (not to be confused with binary status effects like Blind) can be classified as follows. Buffs from different classes can stack, while buffs from the same class do not.
Class A: usually affect a single stat (e.g., ATK down)
Class B: usually affect multiple stats (e.g., ATK/DEF down)
Class C: rare and usually limited to certain SSR kamihime
Eidolon: includes temporary Eidolon and Burst effects
Stacking: accompanies skills with short CDs and small effects, and can stack to the specified amount

List of skills by stat affected and class on JP wiki

Debuff cap
A debuff cap of -50% attack and defense is currently implemented in the DMM version, but not the Nutaku version (as of 8/8/17) [Source]. Expect the cap to be implemented by Feb 2018.