Does my ex pity me, does he want to be friends, or could he maybe want to try things again with me?

Yes you shouldn't have offered to take him out. Greeting someone hapy bday is one thing. Offering to take him out if they're desperate on their bday is another. It is wrong if u dont wanna be with him. You care about him and maybe wanted him back before which lit some emotions but shouldnt have offered at all. He's a dude he'll be fine and find some way to celebrate with his boys or whoever. Unless he's a loner. Does he wanna be friends? Maybe? Who cares. He cheated. Maybe he wants you as call later down the line. In rare instances exs can be friend but later down the line. You're best bet is to find someone new if he broke up with you and dont offer to take him out again.