If you don't mind me asking, would I be correct in guessing that the breakup was instigated by you?

To be honest, I don't see where all the restraining order advice has come from. Based on what you've said, I see it somewhat differently.
I think that for whatever reason, he's heartbroken. As you said, you got on really well, chatted all the time, and he quickly moved in. That sounds like someone falling for you pretty hard to do that. And then you broke up, which I guess involves him moving out too.
I expect the reason that he got other people to contact you through dating sites was because of jealousy, and it was nothing more than a badly thought through attempt to put you off being on there.
He's probably popping up all over the place because he wants to see you, or to talk to you.

Have you actually just tried approaching him and saying very casually "Hi, I didn't expect to see you here"

I expect that if you did, you find that he has no malicious intent, he's just trying to force a situation for the two of you to reconnect again.
Either way, approaching him and being very casual about it will allow:
a) Him to say whatever he has to say
b) You to either set him straight or give him another try, depending on what you want.

To be honest, unless there's a direct threat against yourself (which it doesn't seem that there is) I'd say that attempting a restraining order is pretty futile