OH the last thing you should do is confront him. He has nothing whatsoever to do with your relationship with your gf. Their relationship is entirely under her control. It sounds very much like she wants to have her cake and eat it too.

You're girlfriend's actions about her ex are very suspicious. I was sitting here thinking, attempting to remember my exs birthdays and the only one I can recall is from nearly 30 years ago. The only reason I remember it is because it is the day after mine and he was born and St. Patrick's Day (named Patrick).

Are you familiar with the old poem If you love something set it free, if it returns to you it is yours, if it does not it never was?