heya, i finally took a look at it.  in the parenthesis is your translation, everything after that is a tip or what I might say, but you don't have to use my translations

Cater:
Zokuseidan (Elemental Bullet // Attribute Bullet)-------I might say “Status Bullet,” either way works though
Seishidan (Stationary Sphere)----------Stop Bullet
JIraidan (Elastic Mine)----------Mine Bullet (? Maybe like you shoot and it sets a land mine)

Eight:
Kousokuken (Fist of Light)------------Light Speed Fist
Bakuretsuken (Exploding Fist)-----------in the past it has been called “Raging Fist” or “Pummel,” Exploding Fist works though

Jack:
Mikiri(Counter)-----------Mikiri is like one of those stylized instant slashes where they dash+slash instantly behind the enemy, and the enemy just stands there like "wtf happened!?" and dies.  I dunno what to call it.  “Abandon” is the literal translation.  I might just leave it as “Mikiri.”
Mujyou Kousuisetsu(Unexpected Crimson Snowstorm)-------Sudden Crimson Snowstorm
Meikyoushisui(Shiny Waterproof Mirror)----------Clear Tranquil, same as Yuffie

the rest looks good!
going to look at the summons now,