As a male I'd like to offer an opinion, if that's ok.
Three things here.
No-one can decide what's sent to them on their phone. As you'd already crossed the line of privacy - you have btw - you really should have checked his sent messages to see what, if any, response he sent. If he encouraged it, dump the bum. If he sent her a message to go away, you've no issue. It's actually healthier if he sent no message at all. However you do need to ask yourself if you're ready for a relationship with baggage - it sounds like you may not be, (and that's no bad reflection on you at all, just how you're built).
You say he's keeping them - is it that he's saving them or just not bothering deleting? There's a difference.
Now as to porn - that's a different issue and one that I would imagine causes a lot of arguments. But please believe that men - all men - like to have a look at porno every now and then and it usually has zero reflection on their feelings towards their partners. It's simply visual titilation and men do not make the fantasy link that women do. It's now easier than ever to access and receive; when I was growing up in the 70s and 80s it was like a taboo that we all tried to get our hands on. It's like a kid who's been denied sweets for years suddenly being given the keys to a sweetshop. You could ask him to keep it private from you, say on his private pc or private phone, but you will need to overcome your need to snoop if that's going to work.