Personally, I would stay away from fb completely. Let him tell people what he wants. He will in rl anyway, so 'point scoring' on fb is, well... pointless imo.
I think he is doing it as another way to get to you. He may be trying to convince you that he's 'over you' and moving on. In the vain hope that it will inspire you to realise what a catch he is, and beg him to come home. Methinks he doth protest too much, and all that.
As with the silly text messages, ignorant song analagies and false promises, ignore, ignore, ignore.
And then ignore some more.
He is playing games like the silly little boy he is.
However, now it's 'out there' people might start to question you. Be prepared for that. Maybe have an answer ready when they ask. Just tell them as much as you want them to know. I would probably say something like, yes, he cheated on me so I ended it. But it's up to you what you feel comfortable with.
Fancy getting the house sorted today! Well done, you're doing fab x