She still can't defend herself.

He's taking charge.

Okay, she's just suicidal at this point.

No, just particularly clueless about hand-to-hand and general combat tactics. She thinks she can simply intimidate him with the rifle and didn't learn enough from the previous day's action. While shooting a plane to disable it is one thing, (and she is by now a skilled marksman) actually shooting a presumably unarmed person face-to-face is a whole other thing. The discharge was more an accident/panic reaction. And on a deeper level, she's a young person who has been completely alone for over a year and the last thing she wants to do is actually loose the only other person she's likely to see anytime soon.

I had no idea she shot at the plane...

Those little <tap> <tap> <tap> were her shots into the hot section of the turbine, a great way to provoke a catastrophic fire. The only thing worse would have been to hit and cause a break up of the turbine wheel. Most aircraft didn't have any kind of turbine containment, that's why many have a "danger turbine" warning band on them, to show where not to be anywhere near in case the thing goes kablooey.

The latest Star Trek movie has an extreme example of intake dangers.

Also, a lot of chicks don't let guys have nice things.

LOL, I love how he just grabs the gun away... again