"Of what were you thinking yesterday" is quite correct, more than the sentence with the dangling participle.
Though technically correct, that construct sounds quite stilted and old-fashioned, even literary. I don't think I have ever heard anyone ask a question in this way in English.
I agree completely, although the two phrases may have different meanings. "what were you thinking" is often used as a reprimand, whereas "what were you thinking about" is a question. However, they should still accept both options for lack of context
But it's not "what were you thinking?" but "what were you thinking about?" The expression "penser à" means "to think about" and here we find it separated: À quoi pensiez-vous hier ? The English "of what were you thinking" is extremely stilted and although it is grammatically correct, I wouldn't expect to find it among the recommended answers here.
The i in pensiez was not pronounced clearly. I guessed it due to the title of the exercise.
Same. I can't hear it at all in the slow pronunciation, although it is somewhat audible in the faster audio