I am going to break this up into sections to make this easier on... well everybody.

Characters

Terra - Honestly there isn't much I would change about her. Trance/Morph is a good ability, it's just a great ability in a game where it's not really needed. Tweaking the enemies and gameplay difficulty would be enough to make this skill stand out. Other than that, I might actually rearrange her natural level magic acquirement cause I find it silly that she learns some great spells at ridiculously high levels. I would allow her to learn some of her spells a bit earlier.

Locke - I would make his steal/mug command and thief weapons be based on his Speed stat a la FFTactics. It would make his gear and Esper growth a little more important and I feel it would make him more unique from the other brawler characters like Sabin and Cyan. I would also remove his ability to use the Illumina/Lightbringer cause he already gets the Valiant Knife and I like how this makes getting rid of the Ragnarok more of a difficult decision for some fans.

Edgar - Obviously, his Tool Command needs to be nerfed. There are a few ways to do this:

Easy Way 1: Make all of his tools 1X use per battle so you can't spam them. This still makes him pretty strong in the game, but not outright overpowering in boss fights.

Easy Way 2: Redo the damage formula and make his level no longer a factor in it. Instead rely on his stats, as this will make the esper system more practical as well as his equipment.

Medium Way - Make his tools have cool down times in terms of battle. So using AutoCrossbow in a battle makes it unusable for three battles afterwards. The number of battles needed to recharge is based on how broken it is. I feel this would greatly balance Edgar out while still keeping his Tools pretty powerful.

Hard Way: Create a Fuel system, though I feel this would be more cumbersome than balancing. I noticed most people don't like characters who have to keep track of arbitray ammunition in Turn Based RPGs. Just ask Billy Lee Black in Xenogears and Rangers in FFIII.

Other than that, I would probably strip him of being able to use the Ultima Weapon and Lightbringer as well, since he can use the Dragoon combo build. The guy has way too many options.

Sabin - Mainly nerf Blitz a little more, either by making them cost MP, or weakening it by changing the damage formula.

Celes - Like Terra, I wouldn't mind if her acquisition of natural magic spells was a bit more convient rather than having her learn Meteor at Lv. 99. Beyond that, I would work on Runic. My favorite choice would be to just give her a Relic or two that changes the Runic command around. My favorite choice would be for her to have it work like an Counter Magic ability if a spell is used on her. Another intriguing choice would be for her weapon to be endowed with the properties of the spell she absorbs kind of like the Mystic Knight class in FFV.

Shadow - Power down his Throw command, he does way more damage than he should with Shuriken, or you could jack up the price of his throw items by ten fold. Other than that, he's actually pretty balanced.

Cyan - Needs a new input system, my favorite idea would be to adapt the Super Combo move from Breath Of Fire where you have a short amount of time to input certain commands and depending how many you get in will determine the move he uses. Granted the game will tell you as you input them that you've put in enough to reach the next rank of his Bushido. Either his levels or a Relic can increase the amount of time for you to input commands. I also would allow the Gauntlet Relic to work in his Bushido moves.

Gau - He needs a glossary to tell you what each of the Rages do, and the player needs to be able to customize the list. One option would be that Gau can hold maybe 10 Rages at a time from his overall list so you don't have to get unnecessary hits while your cycling through his huge list of Rages. They already got rid of God Wind Gau mode so he's pretty tame now. Though I may still feel some of his Rages need to be nerfed.

Setzer - Make all of his Gambler weapons have secondary effects to offset their crummy attack power and his average stats, and maybe give him a relic to power up his slot ability.

Mog - Needs a relic to increase the success of his dance. I also feel some of his dances need to be reworked cause half of them are pretty worthless while the other half is devastatingly powerful. There is no middle ground with them.

Strago - Needs to have his Lores spaced out better in the game. He only gets a few worthwhile ones in the WoB and most of his really good ones are wasted because you can get his ultimate Blue Mage skill right off the bat in the WoR after you recruit him. Perhaps make some earlier boss also use Force Field and prevent Strago from doing the Hidon quest until he gets the majority of his Lores first. He also needs better magic enhancing gear, he gets the short end of the stick among all the mages.

Relm - Is honestly pretty balanced. I know people whine about sketch but if you are not using the Fake Mustache relic with her, you are simply using her wrong. I can't really think of anything to make her better without making her broken.

Umaro - I wish you could use Green Cherry's on him to make him stronger like in his boss battle. That would actually be kind of cool, to allow you to use certain items to temp raise certain stats or add properties to his attacks. It would make using him more strategic.

Gogo - Probably give him a better weapon/equipment pool, maybe some relics that can increase his ability with other party member skills.