Within our relationship he changed his mind 5 times, not knowing what he wanted.
OP - don't fool yourself like this.
He knew EXACTLY what he wanted.
He wanted to undermine you, to keep you insecure & desperate.
He wanted to make you play the Pick-Me Dance as to whether he "wanted" to be with you, & escalated to making you Pick-Me Dance with threats/actuality of Other Women.
www.chumplady.com/2012/04/the-humiliating-dance-of-pick-me/
You need CHUMPLADY!
Here are some other instructive tales of Pick-Me Dancing - www.chumplady.com/?s=pick+me+dance
& when you have time, browse through the archives - ChumpLady is wise, supportive, snarky ... & often hilarious - just what you need right now.
Why do I miss him?
That's not love my dear - it's a Trauma Bond.
www.counselling-directory.org.uk/memberarticles/trauma-bonds-what-they-are-and-how-to-escape-them
Stop beating yourself up about it - it's very common. A kind of Stockholm Syndrome. Your ex manipulated, controlled & gaslit you til you thought down was up.
Part of what makes it hard to let go is the Hoovering an abusive partner does to continue to exert control over you - lonerwolf.com/hoovering/
Just like he blew hot & cold in the relationship to keep you disconcerted & focused entirely on him & his wishes, he is now doing push me/pull you because he can feel his control slipping & wants to reel you back in.
About 3 weeks ago I met someone new - taking baby steps but he's lovely.
No more than baby steps until you are safely away from your abuser.
There is no way you are going to heal while you are still having to cohabit with him. Put all your energy into avoiding your ex as much as possible, into expediting the house sale, into using Grey Rock to stave off your ex's manipulations - www.e-counseling.com/articles/what-is-the-grey-rock-method/
My ex doesn't know about him. Now my ex has made a massive U-turn saying he loves me, wants to marry me and have kids straight away. Promising he won't change his mind again - I'm trying to stick to my guns and focus on the future, but I just can't get my ex out of my head and now doubting the new guy.
Don't conflate anything your ex has done, is doing, or says he will do with your new guy.
Can you see how bonkers it is - that just because your abusive shit of an ex is now Love Bombing & Future Faking you (again) that you imagine that has ANY bearing on who new guy is what might develop there later?
I keep thinking what if I've made a mistake?
The only mistake you can make now is allowing your ex to Hoover you back.
He is poison to you.
What on EARTH makes you believe you can trust one word from his self-serving, lying, cheating, selfish mouth?
Why do I miss him? Or is it just because we live together and I can't escape from the situation.
See Trauma Bond - & yes, it is going to be very difficult to naviagte keeping yourself safe from this emotional predator's abuse while you still have to cohabit.
I don't want to make a mistake in case he really has changed but I have no idea how to make the right decision!
GIVE YOUR HEAD A WOBBLE!!!!
Sorry to shout OP - but WHY are you fooling yourself that your abuser will CHANGE?
THIS IS WHO HE IS.
Coercive controllers don't change. They just escalate.
What's the situation with the house sale?
Are you getting viewings?
Is your ex pleased to be selling or is he obstructing any part of the process?