There's a few things that you wrote that seemed a little unfair. You say that you were this horrible person to him during the depression, and you broke many promises. He stuck by you for a long time during that.. this must show how much he thought of you. You then say that you have a hard time getting past the harsh things he said when you broke up, despite him apologising. Do you think that you may be being a little unfair with this? He seems to be able to forgive enough to move on, and try again with you. I think you should try letting go of some of the past too, and try again with a fresh outlook.
I think too that you do not understand the taking it slow thing. To say that you do not like that you're no longer the center of his universe, and that he goes to see friends, but this is exactly what taking it slow is. Perhaps if you did what Hamster suggested, build up your own life, interests and hang out with your friends too that you may not be thinking this stuff over and over and dissecting everything he does or doesn't do. Just try enjoy being together when you are, building up trust, having a good time and creating some fun, wonderful memories to take over the hard past that you both had together.
I also think you need to keep working hard at the therapy. Low confidence is a horrible thing to suffer from, especially when it effects us so deeply as to obsess over him liking a photo on tumbler or overthinking things with his actions. You need to also learn to trust him and his word when he says he wants to be with you - these things will be a little easier with working on your own self confidence and sorting through your past issues. I know that's so so so very hard when you've been through everything that you have, and its going to be tough. But please, keep working with the therapist and remember to be kind to yourself too. You've been through a lot.

As for your family, just tell them if you hate lying. While they do not like him, am sure that they will be happy if you're happy. They obviously only see one side of the story, your side, and that you probably told them when you'd broken up and were angry.

Good luck with everything.. and please try to relax and just enjoy being together.
Hugs