Answer:
Mary and I went to the library.
Step-by-step explanation:
Mary and me ⇒ This is grammatically incorrect. When describing someone and yourself, we say [their name] and I.
Mary and himself ⇒ The correct way of saying this would be "Him and Mary".
Mary and her ⇒ "her" is a determiner, so it would have to say "Mary and her dog" or "Mary and her mom", etc. to make sense.