Did I (21) ruin my chances with my ex (24)?

So a week ago, I had a huge irrational fight with my ex (which I will admit was mostly my fault) that caused him to break up with me. It started out with something SUPER trivial and then just exploded from there. Some things I said in the argument is definitely not what I felt (i.e. I hate his family... It's not that I hate them, I just didn't like way they treated him) and he took real offense to it.

After he broke up with me, like every desperate ad emotionally attached girl, I begged and pleaded with him to get back with me, and he said 3 things that really don't mesh with each other:

1. He likes me, but only wants to be friends at this point
2. That he'll try to reignite what he used to like about me, to try one more time, and to act like a new couple 3.Respect his decision when he doesn't want me to touch him. I really didn't get what he was saying, so I was talking to a mutual friend of ours. The mutual friend brought it up to him (in hopes that he could help us out with our situation) and so when I decided to talk to my ex about this again, my ex said he was even more mad at me for involving friends and family into our situation, since he doesn't like that. Again, he then reiterated the 3 above statements and forewarned me if I ever brought up this subject again that he would just leave.

...Uhm. So, do I even have a chance at this point, and what are we even, anyway? I'm going to assume we're broken up, but why did he said he'd try again and then not even try???

Oh, here's some other info: 1. I'm 21, he's 24, but he has no job, driver's license, and hasn't graduated from community college. 2. Because he has no money (usually), I was the one who paid for most of our meals. 3. Because he has no driver's license, I was the one to drive us to places. 4. He has a pretty toxic family and one day called me crying about how he couldn't take it anymore. At that point, I let him live with me at my grandma's house (with permission), even if I maybe wasn't ready for this. But because it's not my house, he had to be with me 24/7 cause I couldn't leave him alone in the house.

I eventually snapped because of all of the above, went depressed and suicidal, and he broke up with me because he said I scared him... Then also added on a later date that he didn't feel like I appreciated him and I was too controlling.

I guess, I still would like to try again and see if we can improve on our relationship, start fresh. But... If you were in his shoes, would you actually give it another chance?

Also, I'm trying to do the No Contact with him. For those that have tried it... Does it even work?

He has been IMing me on FB asking if he left his charger at my place (he didn't, he told me later) on one occasion, then asked how my trip was (I went on a family vacay), and if he left his case at my place a day later. But that was 2 days ago, and he hasn't talked to me since. I see him online FB and he sees me online... I think?

But yeah, he's not talking to me since then. I've been cordial to his messages, but haven't been engaging him in conversations, ending it with a, "I'm busy right now, but let's talk later!" sort of message. After my 2nd time messaging him in a similar fashion, he has stopped liking my statuses and pictures. Guys: Did I do something wrong? Maybe, what is he feeling?

I don't know. I do want to try again, despite all the flaws. I guess a little part of me believes he can change for the better and I can grow up, too, and I'm a little heartbroken because I did share a lot of fun memories with him.

tl;dr: Mandatory summary/question!

1. Got into a huge fight (my fault) with ex, he broke up with me. Says he only likes me as a friend, but then says he'll try one more time and to act like a new couple, but then also says to respect his decision for me not to touch him. Are we even together? Can I get him back?
2. Does No Contact work with getting a relationship back together? How?
3. He was contacting me for a little but I used No Contact on him (in a special circumstance) and he doesn't talk to me anymore. Guys, what is he thinking? Is this good or bad?