Sweet, new flevel patch with the extended save points. Time for another quick vacation in the world of New Threat. Thanks, Sega Chief.
Edit: On innate abilities @Sega Chief.
I feel that they should help reinforce the character's intended role by rewarding players for playing well and surviving. In that regard, your initial ideas are pretty great. Here are my thoughts and suggestions. Most of this is without % chance or a critical health requirement, but I'm fine with either if it makes things fun.
Cloud: An all-rounder is tricky, and the fact that he's the party leader for the majority of the game means the innate ability should be straight forward. Maybe a mild bonus to party Dex or Spr, like a stack system granting a +1 each turn, max +20 (or more every other turn depending on how the turn counter works). Makes long fights a little faster and safer assuming you aren't constantly losing characters.
Barret: The proposed Vit and Spr stack when attacked is pretty great. I'm wondering, though, if it would be possible to have his innate be based on row placement. It'd be interesting if Barret, a normally one dimensional tank, had an in-battle offensive and defensive wind-up mode. Front row = str & mag; back row = vit and spr. Go full tank, or go bruiser.
Tifa: She should get some kind of Dex bonus/stack if she uses the attack command and hits an elemental weakness. If that's not feasible, then a str bonus/stack while at full health would be a nice mix-up to her typical "critical HP" shenanigans. If you find some way of making the innate ability based on Rank Up, she could have a party leader version that grants a stack of Str to the party each turn.
Aeris: Get a stack of Mag every turn while at full hp or when you remove a negative status. I still like the idea of healing x2, though.
Red XIII: Attacking should grant a debuff stack of some kind. Maybe Mag or Spr debuff. If debuffs would be too much since they don't go away if Red XIII gets KOd, hitting an elemental weakness with magic could restore a small amount of MP back.
Yuffie: Attacking should grant a debuff stack of some kind. Maybe Str or Vit debuff. If debuffs would be too much since they don't go away if Yuffie gets KOd, hitting an elemental weakness with an attack or magic could remove a negative status effect from Yuffie.
Cait Sith: That Rage system would be crazy hype! You are a god if you pull it off. If not, I'd settle for something simple, like getting a stack of Vit/Spr for casting spells.
Vincent: Innate resistance when in a limit form is great. If it's just one element, maybe it should be immunity since you're still losing control of Vincent? Well, I tend not to rely on limits in the NT Mod anyway, so I'd prefer if the innate ability wasn't restricted to the limit break form. Something like recovering a little HP when hitting an elemental weakness with magic, or gaining a buff if a negative status is successfully resisted.
Cid: Luck boost sounds awesome. Luck stacks every turn up to a max would be the happy middle ground, but I'm totally cool with 2x luck. Cid for party president.