"Where is her milk?" is that okay, or would that mean more like "Где её молоко?"
Russians often use constructions like "у неё" instead of possessive pronouns (её). For example, you can hear something like "У меня мама любит кофе" instead of "Моя мама любит кофе". So I would accept "Where is her milk?" here, too. It is up to the course developers, though.
Yes, that would mean "Где её молоко?" implying that the milk might not be with her.
Kind of an awkward sentence structure in English, perhaps it's just me. I would have expected most to say "Where is her milk?" instead of this.
This sounds weird, as if opposing like "she has no milk here, but where does she have it?"