I see why you are irritated but if she is with you it’s because she wants you and not that guy. Relationships are like that, people tend to get in the way when they see two people successfully dating, that has happened to me multiple times. Some key points that I got from reeding your post:
She told you: that’s always good, she told you because she doesn’t like it either.
She told you she hangs out with him because she feels bad for him: believe her, if she liked him back she wouldn’t have told you about any of this considering you don’t get to see her that often and the two of them could just hang out all the time.
Age gape: the only thing you should be concerned about is the huge age gaps that there is between them, not because of her but because of him. I’m not saying that aLl MeN are the same but men that like younger women just want them to have sex and not to marry them or be their friends.
If I were you I would just trust her. You will show her how much trust you are putting into the relationship. If she’s a cheater she would have cheated on you by now but instead she told you about him. Keep that in mind. Good luck.