Cheating/breakup

So after my now ex partner cheated on me while I was 14 weeks pregnant I decided to give him a chance but once a cheat always a cheat right. Anyway I was on his Facebook and seen he’s deleted a lot of messages since he’s always online on Facebook messenger not messaging me and all the messages in his inbox are old, anyway it also has an option where Facebook connects with your contacts and a lot of girls showed up there, he’s also been sending friend requests to other girls. He’s meant to come stay over at my house on weekends (we don’t live together) but he’d just turn his phone off and go out probably to the clubs, and then call me at 4 am like he hasn’t done anything wrong. Am I over thinking things or is that deffo a sign he’s back to cheating?

Anyway I don’t know how to go about letting him see his daughter when she’s born or if I should just cut ties completely, nobody even knows we’re having a baby apart from his friends and when he first found out he said get an abortion but then changed his mind and keeps saying how’s my princes etc but he wasn’t keen to announce it on Facebook or let me tag him in the scan picture weird right? So anyway I think he uses Facebook to cheat on me that’s probably why

If this was your baby’s father would you let him see the child or wouldn’t you just be a single mum?