Pronouns are tricky. The writers on DC's superhero TV shows use nominative pronouns when they should have used accusatives and accusatives instead of nominatives, even when they are putting words into the mouths of reporters for major metropolitan newspapers.
Pronouns come in families. "She", "He", "I", "We" and "They" are in one family and "Him", "Her", "Me", "Us" and "Them" are in another. Mixing them is like putting a Montague and a Capulet together.
It doesn't have to be. Both English and Russian are using nominative case. So English using her, accusative or whatever, is what makes no sense to foreigners and us actually not grammatical. What is important is how people actually say it. And I believe я и она is how it is said in Russian. Native speaker please verufy.
No, at least not in formal English. Я and она are subject pronouns, like "I" and "she." Me" and "her" are technically "object pronouns," and they have several other equivalents in Russian...all of the other cases besides the "nominative" case. In English, essentially the only words that display any declension (like every Russian noun and pronoun) are the pronouns.
Yes, "I and she" is awkward. However, "She and I" is not. It might not be the most common way of phrasing it, but it is the only way of doing it in/on anything official or gradeable. "Me and her" simply gives the mistaken impression that the people in this exercise are grammatical objects, which they are not. "Me and she" is mixed between object and subject.