Rouky, You are the only one that can determine whether to invite your h over for meals and cake. If you are comfortable in doing so, then do it.
As for the financials, please listen to kml. She's a very smart lady who knows exactly what she's talking about. Sure, right now, he may say that if you sell the house and give him his half, he won't go after your retirement, savings or assets. Even if you get him to sign a piece of paper, when the time comes, he could cry the blues to the judge and say he signed it under duress or when he was on hard times because it's the only way that he could get the money from the sale of the house.
I would make darn sure that anything that happens pre-divorce is handled by a lawyer and is legally binding because anything at this point could changes, especially after he gets his hands on his share of the house sale. You can be fair about things, but you need to ensure that you are legally protected. No one is saying to take him to the cleaners, but we are saying that you need to have a legally binding agreement in place and that may mean divorce.
Yes, I do understand that you don't want a divorce, but there are times when one may be necessary in order to protect the assets, etc. If he should ever get his act together and want to reconcile, you can then decide if you want him back and remarry.
He had choices and he made the wrong ones and now...he has to face the consequences of his actions and sometimes...they have to lose everything before they come to realize that what they had was what they were looking for all along.
For now, you have to focus on you, your children and especially your monetary assets.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.