Several different issues here. For a start, you're self-harming and you sound very mentally fragile at the moment. I'm sorry your family are not more sympathetic, self-obsession is a pretty natural condition in teenagers, and it's also a very unkind way to refer to real problems. Is the counselling helping?
Issue 2, the ex.
I can't help but feel sorry for him as I feel no one else does, like he is my responsibility and he has so much potential that's being thrown away.
If you can nip this tendency in the bud right now, you'll have a happier life for it, believe me. What you have described is being a Rescuer. It's a role that women, in particular, are conditioned into - they are encouraged to have compassion, be understanding of others' motives, give people a second chance etc etc etc.
Bullshit. And don't let anyone (esp female friends/family members) tell you different.
Obviously there are times in life where compassion and second chances are good. But they will generally be screamingly obvious. You do not need to waste your precious mental energy forgiving and understanding some dickhead who spreads rumours about you, no matter what a horrible home life he has. You're tying yourself in knots to do it. I'm not sure I even understand this:
he is still that (not so much in reality) gorgeous, funny, kind-hearted boy inside despite all the things I hear.
I'd probably go with all the things you hear, to be honest. Don't project good qualities, or assume that because someone is being horrible on the surface, they must be nice "really" underneath. No, they really can just be horrible.
And you absolutely must not mend fences with him. Be honest with yourself, it would be horrifically painful, because you're not over him. At some level, you probably enjoy the obsessing and the projecting - it's familiar, it gives you an emotional hit, it keeps you artificially "involved" with him so you can cling to the notion that there's still a relationship of sorts there, even if it's a one-sided one. But ultimately, this is a waste of your time, and you can do the difficult, tedious work of changing your thinking pattern to get rid of him from your thoughts. It will be hard and there will be a lot of backsliding (been there) but it really is possible.
Some of this post might be helpful, although it's mostly talking about relationships that have never happened rather than ended ones - the important point it makes is that obsessing about somebody is a choice. And you can change your mind.
As for new bloke, if he's not floating your boat, then dump. Sorted. Nothing wrong with just not finding someone appealing.