B. Me , direct object.
Jeremy bought Patrick and me tokens for the games.
Me vs I.
Assuming that Patrick is not part of the sentence.
Jeremy bought me tokens for the games. THIS IS THE CORRECT ONE.
Jeremy bought I tokens for the games.
Me is used as a direct object because a direct object receives the action performed by the subject.
subject = Jeremy ; verb = bought ; direct object = Patrick and me.
The second sentence is correctly edited. I hope this helps!
The subject would be "we" since that is who is seeing the movie (the movie would be the direct object)
Hope this helped!