Not a native speaker, so take with a grain of salt unless someone verifies:
But, I think it's because of passive action in the Russian sentence. It's not about her hurting her hands or injuring her hands by her own action - her arms hurt on their own, through no fault of hers.
I think you'd have to use the verb form ранить (to wound/injure). This sentence just means that her hands aren't hurting/sore/in pain.
Yes, actually it can. But this sentence would sound a little bit less natural.
In this sentence you put accent to 'никогда' and it sounds like you are little be angry because of this fact:)
Genitive. Nouns ending in а end in ы, but in this case it is и, because you cannot write я or ы after the "seven consonants" (к, г, ш, щ, ж, ч, х)
I'm pretty sure it is nominative plural, since the sentence is about her arms.
(Genitive plural would be рук, but i don't see a reason to use that here)
Her arms are so strong that they don't feel pain?, or are her arms so weak that they can't inflict any pain?
Although the meaning is pretty much the same, I think the grammatical structure is just too far off.
The subject is 'her hands', not 'she', and the hands aren't sore (adjective), but actively hurt (verb). Or a negation of that, in the exercise.
I also thought "She never has arm pain". The "У неё", always makes me think "She has".
You might hear people say "Her arms don't hurt" or "Her arms have never hurt" or "She's never experienced pain in her arms", but it would be rare to hear "Her arms never hurt" (at least from where I've lived in the US).
I'd expect that in a sort of narrative situation.
—Why didn't she go to the doctor earlier?
—Well, her arms never hurt.
I selected EXACTLY the words above from the word bank, and it was marked wrong - the SECOND TIME in this lesson. C'mon, Duolingo, pull up your socks a bit.