impressive shooting!

question for someone who knows about such things: is her posture normal for shooting a rifle? at 1:15 and 2:09 she seems to be arching her back backward with her hip forward. It looks really unnatural.

I'm not an expert, but I've shot a lot of rifles and have some gun-nut friends. Basically, NO, that isn't a normal posture. However, it seems quite effective for her.

She is basically using the shelf of her pelvis as the "ground" point of her elbow, almost like the function of a tripod if you were going to shoot while prone. That isn't normal, but then her hand position on that arm is even weirder -- she is propping up the rifle with what looks like middle and ring fingers making a "v" shape, then pointer just in front of the trigger guard, and thumb on the trigger guard / lever. Very very weird -- in general most people would put that hand further out along the barrel and just grasp the wood there. That would normally be more effective because the wider the distance between the contact points with your hands, the more steady and fine your aim can be. BUT, she obviously knows what she is doing and is using the stability provided by resting her arm on her pelvis to overcome that. She's a way better shot than me, so I wouldn't classify any of what I've said as "criticism", just noting that she does certainly have an unusual style.

By sound and size, the rifle is probably a .22. A .22 that size can be quite light, which would work well with her style of holding the weapon. I'd imagine that trying that with a bigger rifle, especially with a longer barrel, would be uncomfortably heavy on the fingers she is using to prop up the weapon. Plus, higher calibers would kick enough to necessitate actually grasping the forestock instead of just resting it on fingertips.

Even when I was warned against kick and barrel-rise when shooting an AR-15 (basically an M-16), the first time surprised me how much the weapon will jolt upward on rapidly fired shots unless you are ready to compensate for it...

I'm not an expert, but I have watched the Olympics.
Her shooting position appears to be typical for a competitive shooter firing from the standing position.
Check out the "Shooting Position" section of this page:
http://www.issf-sports.org/theissf/academy/e_learning/rifle.ashx