Yes, in this particular case. In principle, the accusative form is exactly the same here. But be careful: there are two forms of this word (in both cases): "неё" and "её". In all instances I can think of right now you would use "неё" whenever these cases (genetive or accusative) follow prepositions.
Native russian speaker here, I second this. You just have to pick up on the intonation to figure out whether it is a statement or a question. This happens in English, too. Imagine someone saying:
They have a bike now? (question)
They have a bike now. (statement)
I hope that helped!
Russian has a peculiar way of expressing possession, which I already described earlier in this thread -- please read the entire thread before posting duplicate questions. In any case, I am quoting myself:
The Russian way of saying "A has B" is "У A (genitive) есть B (nominative)" which literally translates into "B is by/with A".
Most likely you've made a typo somewhere. Once DL thinks you are wrong, it tries to "recover", and the version it offers may not always match the one you had in mind. Nor it is always grammatical, like in this case: DL has probably a hard-coded rule that "she's" is an acceptable short-hand for "she has" (which it is in expressions like "she's got...", but not here), and then it suggests it even when it's wrong.
That's just how Russian grammar works. "Y" pretty much means "with", and "неё есть" in that context means "she has/possesses". So the direct translation would be " With her she has a (insert item)", but we just say "She has a (insert item)".
I didnt invent the Russian language, so I can't tell you why this is what you use in this case, but you just have to learn that this is the correct usage of this type of sentence.