When divorced, and the house it not paid off, how does the judge decide who is responsible for paying off the house, and how is it split of there is still an amount owing. Also, if a child already has a father who is paying child support to the mother, is the new husband still responsible for paying child support after divorce.

If the new husband is not the child's father he is not responsible for child support.
It is pretty much up to the Judge how he splits assets and bills. Typically the bill is paid by whoever's name is on it. With the mortgage it could be more complicated.

Make sure to get your name is off anything your ex has agreed to pay off. What the judge says means nothing to the creditors. They hunt down anyone who is on the original contract and care not if a divorce has occurred. They just want their money.