7. The professor and myself met for a review session.
Correct! The sentence is not grammatical. The answer is NO.
The subject of the sentence -- those doing the action in the sentence (meeting) -- is "professor" and "myself". Since "myself" is occupying the position
of a subject in the sentence, the word "I" should be used. "Me" or "myself" would be appropriate if it serves as the object in the sentence. For example: "The professor met with me."
So the sentence should read: "The professor and I met for a review session."
Correct! The sentence is not grammatical. The answer is NO.