Ask the court to change the custody order.

Do NOT sign the Interspousal Transfer Deed - especially if he made mortgage payments during the marriage. If the house was completely paid for...

You first need to establish Conservatorships over them. Here’s a link with info: https://www.courts.ca.gov/selfhelp-conservatorship.htm

If they settled and dismissed the case, then they should not come after you.

Did she lose custody or did she lose her parental rights? If custody, you would seek a Guardianship - not Adoption.

He could arguably ask for what are called “Jackson credits” for the one month but it is rather cheap and inconsiderate and he is unlikely to get...

....as long as dad was available to receive him.

You can leave; you just can’t take the child unless the other parent agrees.

It’s a percentage based on equitable value of house at time of marriage compared to payments to principal during marriage - thus creating a ratio...

If you are actually living together and you are contributing to the expenses, then she shouldn’t.