Since it's always good to have a clear understanding of grammar when learning a foreign language, I want to chime in here. The inversion of the sentence structure is irrelevant; what matters is what the "who/whom" word is filling in for.
If its a direct object, then you use "who": He is singing/Who is singing?
If it's an indirect object, then you use "whom": He is singing with her/With whom is he singing?
And it's definitely not as widely used as it used to, but if nothing else, understanding the distinction will help clarifying indirect and direct objects which can definitely be confusing in a new language.