I am really confused whether a preposition is needed before a question word and I want to know which one is correct:
"Ask your teacher about what she is going to put in the test"
"Ask your teacher what she is going to put in the test"?
As is often the case, they are both correct but mean slightly different things.
'Tell me about something' literally is asking for a description of something. It is an indirect way of asking a "what question". A student might ask this way because they know the teacher won't tell them directly what will be on the test (note on not in). Asking to be told about what is going to be on the test could be answered by the teacher describing, in more general terms, the material that she will be putting on the test. This might include mention of the subject matter ("The stuff from Chapter 2", or perhaps "3 sliding friction problems and a centripetal force problem").
'Tell me what...' is asking directly for the contents of the test. And is unlikely to be answered by the teacher.