I don't personally suspect mites, hamsters do scratch and groom quite a bit. Her fur also looks to be in very good condition, not something I'd expect from a ham suffering with mites. Her being so jumpy is likely due to her not being completely tamed yet. If the nervousness started two weeks after she was brought home, you can rest assured that it's not unusual. Many hams won't express their nervousness for the first few weeks as they're still in a bit of shock from being brought home. The heat could also be agitating her as well. I wouldn't recommend a frozen water bottle as their tiny paws can get stuck or even get frostbite if they are pressed against it too much. Instead, try offering ceramic mugs and tiles or a terra cotta pot. You could also refrigerate a sand bath and offer that to keep her cool
Chilled fruit is fine, but not too often as fruits are sugary. I wouldn't stress out so much, it sounds like you're a very good and attentive owner. Just try moving her to a cooler room, and use as many techniques as you can to keep her from getting too hot. Good luck