Yes, at least some of those tick the boxes for emotional abuse, especially the lying, blowing hot and cold, belittling and gaslighting you. This is why you are so confused and feeling such a strong emotional response- because he has got into your head and is playing with you. I don't think a lot of PPs are showing much understanding of how emotional abuse works. Constantly questioning yourself is part of it.
I recommend that you absolutely, definitively block him. Do not put him on the baby's birth certificate whatever he says. Do not, under any circumstances, give the baby his surname. Tell him that you will only agree to him seeing the baby if he attends mediation with you and work out a written contact agreement together THIS IS VERY IMPORTANT AND HAS SAVED MY DS FROM BEING FORCED TO SEE HIS FATHER - who has gone on to do much, much worse stuff, from which I have been able to protect him because I stood firm.
Read "Why does he do that?" by Lundy Bancroft. Find support from either Women's Aid or other domestic violence support groups.
Accept that you will have intrusive, obsessive thoughts for a long time, but you will be free one day (I am free now). These are not a measure of how much you are meant for each other, but of how much he has managed to damage you.
People do not uncritically adore him as much as he likes to make out, believe you me. If you are forced to observe him for some years, you will see the penny dropping for more and more people over that time.
Visualise a strong, impregnable wall between him and you and DS.
I'm sorry about some of the responses you've got here- the Relationships section is usually somewhere that you can find a lot of posters with experience and knowledge of emotional abuse- but not today for some reason 🙄