Learn Russian: Кто он? Он студент?

In Russian, the present tense of the verb "to be" (am, is, are) is usually skipped. So, Кто он? literally means "Who he?", and Он студент? literally means "He student?".

Why do we use Кто here instead of Что?

The word Кто means "who" and is used exclusively for living beings, like people and animals. If you were asking "what" an inanimate object is, you would use the word Что instead.

The words in Он студент? are in the exact same order as a normal statement. How do we make it a question?

In Russian, you do not need to change the word order or add helper words like "is" or "does" to ask a yes/no question. You simply use a question mark in writing, and when speaking, you raise the pitch of your voice on the key word you are asking about (here, студент).

Would Кто change if we were asking about a woman, like "Who is she?"

No, the question word кто does not change based on the gender or number of the people you are asking about. "Who is she?" is simply Кто она?.