Welcome to the forum, Omar.
Please ask only one question per thread. You will notice that I have changed your thread title. 'Grammar' is not a suitable title for the phrase you are asking about.
Your first question should be 'What's wrong with "me neither"?
First, let's be sure that your profile is correct. As an Egyptian citizen, is your native language really American English?
Please tell us why you are asking these questions. If it's a homework assignment, it's against the rules for us to help you.
Student or Learner