Kensai, welcome to FFH, and thanks for playing! Allow me to respond to your feedback, and I hope it clears things up:
First Aid is actually only a few points weaker than Cure, but is based on Physical Attack and is free, and cures debuffs on the user, making it useful in different situations from Cure. It's not meant to be an amazing ability, since it's one of the first ones you get. That being said, it's still really good early-game and in situations where you need to top off your health.
To clarify, the 13 AoE you see is the game's way of saying "summon AoE", basically, 2 AoE instead of 1 or single-target. This was to put it on par with Whirlwind and other around-self skills that had an AoE boost. Unfortunately, I'm having trouble setting them back to default. Even when I set everything back to how it was in Vanilla, they still act strangely.
Magicbreak is meant to be used to cripple mages while you go after other units. If you can't flat out kill the mage, making it unable to cast spells (or at least, as many of them/the stronger ones) is a viable option. The Breaks are all weapon range and work great with Bows, for the record.
Thesis Hunt has always been a weird mission to balance. No matter what changes I make to it, it always comes out ridiculously hard or ridiculously easy. I've never been truly happy with it, but I'm getting there! The one Thief did lose Counter and Maintenance, and the other had Counter replaced with Arrow Guard. I noticed, however, that he didn't have any actual Thief skills. He can now steal your gear, but I'll see during testing how that plays out. Nurse is staying, namely because I don't feel it makes the battle much different one way or another.
I'm aware of the bug with the stat down skills, though I'm not sure why it's happening or how to fix it. Darth looked at the ROM ages ago and saw that it should be working perfectly, so I don't really have an answer on that just yet.
The hourglass buff on the Soldier was like the result of the Fighter in that fight using Cheer, which Adds: Boost onto an allied unit to increase their strength. (Think Helping Hand from the Pokemon series.)
In regards to Scream, it's getting buffed in the near future, I'm just not sure what I'm going to do with it. Fret not, it's on my list!