I am sorry, but none of these is correct. What was your nightmare about? (was, rather than is, as presumably if you are asking the person this question, they are awake, and the nightmare is in the past, not the present). You wouldn't really ask 'what is his anxiety about' - either, what is he anxious about or what is the cause of his anxiety. What are her dreams about? This is an odd question as why would you be asking a third person about someone else's dreams. Also it depends a bit on whether you mean literally, what did she dream about (while she was sleeping), or are you asking what are her dreams (for the future).

You should say like: What about/is your nightmare? What about/is his anxiety? What about/are her dreams?

You don't need to use is/are in all these questions.