Oh, goody, so at least one thing I had in my original writeup of this review is gone already. For future reference, mousy is pretty much only used to describe a personality or hair color, doesn't really mean much from a skin/build perspective.
Now, for history. The fighting over Hell was mostly part of the second and third wars, so far as I know there was no major action there during the fourth war, which is how you have it written up in your third paragraph.
The last bit of the history also needs to be reworked a bit. Like has been discussed, at this point, the ship is basically a exploration and potential colonization locator, it has nothing to do with "growing Elysia to glory" just yet.
The fighting skill should be retweaked to make most of it not involve the military again. If she received her weapons training from the military, she received the standard training, not training with the odd weapons. Makes more sense for those to be things she learned on her own, with her just receiving basic PA training from the military.
The rest of the skills look okay, but you have 9 all told. I'll leave it up to
@Semjax to decide whether or not that's okay.
I'd probably skip over the Neutrino ammo for the Pestris. Wouldn't see much use unless you were facing an armored target, and if they're in armor, it's probably radiation shielded, so neutrinos wouldn't do much good.
You should also add some personal items here! Clothing, keepsakes, and so on. You're not military, so you're allowed to go kinda nuts with what you have.
Outside of there, looks good to me.
Just a bit more tweaking to go.