complement of a language-nfa
Your teacher is right. $\delta^*(q_0, w) \cap (Q - F) \neq \emptyset$ does not necessarily imply that $\delta^*(q_0, w) \cap F = \emptyset$. Question 5 says that you don't terminate in any of the accept states, question 6 says that you terminate in some non accepting states, but NFA can still terminate in some accepting state.