YOu don't need to sign anything, and you didn't... HE needs to realise HE is the one doing damage here and I think you are conveying that well.
YOu are learning to intimidate him now... And you can see him retreating and running.
He is likley NOT used to that in you...
You can if you want for an exercise open up each of his statements above and script a response to it... You will likekly hear these again.
Having a good truth bullet for each of his comments is great preparation.
"Can't we be adults?" - Adults don't cheat on their families. And they would at least have the maturity to own it if they did. Bye bye. Close the door (no slam, just close it)