1. I think you should take his hints if you think he likes you, but don’t jump at it entirely. Be there for him. Invite him over, comfort him if he’s not over his break up (which if it lasted a while, he may not be). He’ll probably be more likely to open up to you the closer you get to him, and then you’ll surely know if he likes you or not.
2. It’s going to be hard to get things to be the same again if it’s been damaged by fighting. Fighting can really leave some pretty deep scars, but they aren’t always permanent. What you have to do is take steps. First, talk to her about it and make sure you both want to make this work just as much as the other. Next, try not to fight as much. Talk about the things that used to make you guys really happy talking about. Just take the time to get things back to normal, and work with her on this.
3. He probably doesn’t know if you want to talk to him. Exes can be a sticky situation and he’s nervous about opening up that can of worms again, and he knows that just because he’s ready, doesn’t mean you are. So he’s probably just being cautious and careful, and wants you to give him a sign that you want to talk to him again. Try making the first move and talking to him first. It’ll ease his stress and stop the guessing games.