Hi and welcome!
Well I think the first mistake was letting him have a 'fb' in the first place

Anyway it happened and it's what you do next that's important.
Going by his behaviour, how are you supposed to trust him? You need to make it clear you wont tolerate any of this behaviour linked to him chasing up other people online. Although I don't condone checking his personal stuff, I guess on this occasion it's lucky you did!
You said you don't love him....if you don't believe you can love him again and he is chasing other people anyway, I see very little reason for you to stay together. You will just end up old, lonely and bitter. I think it's way healthier to find yourself a job and get the hell away from this relationship!
I hope you do the right thing