Do you have any kids? If you do, keep the pictures. The kids may want to see what their father looked like.
No kids? Do you hate him? If you want to forget as much as possible about ever knowing the jerk, you might want to cut up all reminders.
But it, he, was a part of your life, and you might want to keep the stuff for your own history. You don't need to look at it often, but maybe it will be interesting later. My wife was engaged to some guy before I met her and she is a hoarder so I know there must be pictures of him around somewhere, but I have never seen them. It doesn't hurt to have a box full of stuff sitting around. You can always throw it away, but you cannot bring it back from thrown out.
Certainly sell the dress. I don't know why people keep those anyway except the person spent way to much in the first place. The rings? Rings don't have much actual value. Tiny amounts of metal and maybe a stone or two. If you like the ring, keep it and wear it. My wife still has the engagement ring. You might be able to have the stone reset into a different ring. Or you might be able to sell it. Or donate it. You get to deduct a larger value than you will get by selling.