The sorts of family law cases which can be done on contingency fees are limited by the State Bar ethics rules. If you and your spouse own real estate, you may be able to find a lawyer who will handle the case based on your providing a lien on the real estate.
Peremptory challenges, IF THEY ARE PROPERLY FILED WITHIN THE STRICT TIME LIMITS, don't require any "defense", and can't "fail". If the judge determines that the challenge was filed on time, that's all that's required. IMPROPERLY FILED or LATE peremptory challenges almost ALWAYS are denied.
The finance company is not "obligated" to do ANYTHING as a result of the judgment between you and your ex. They're not required to prepare any deeds, or to remove his name from the loan. You should speak to an experienced family law attorney NOW, so that you don't run across a serious problem further on down the line by five or ten years, when you try to sell or refinance the house.
There's the problem; what you got back was NOT a notice of entry of judgment (FL190) , but a notice of entry of default. (FL 165).
You MAY be able to have the case "un-dismissed" and have a judgment entered "nunc pro tunc" (retroactively) but you'll almost certainly need an experienced attorney to make it happen.
The prior response is mistaken; a third party can be joined, by motion, (now an "RFO") to a California dissolution action. The third parties generally are involved in the custody of children, or have involvement in ownership/possession of community property.
Once the RFO (motion) is granted, the court will issue a summons and pleading on joinder, and then and only then will the summons and pleading be served upon the "joined person".
You may not need an appraiser OR an accountant. You can probably finish it up with some (limited) assistance from an attorney for each of you; you're much better off making sure all the documents are done correctly for each of you the FIRST time, particularly when real estate's involved, than missing something, and finding out twenty years later, when someone's trying to sell or refinance, that something was missed and needs to be fixed.
If you're in agreement on the general framework of...
NO, it isn't a violation of a joint legal custody order, unless the order says something specific about that issue, You've raised the issue with a judge, and it apparently didn't rise to the level of an issue which got the judge to change his order. If there's a joint legal custody order, that means that the court trusts your day-to-day decision making while your child's with you, and your ex's decision-making while the child's with HER. Judges don't like to micro-manage who your child...
To get child support from him, either (a) he's going to need to sign a valid acknowledgement of parentage, or (b) a court is going to have to determine that he's Dad. That makes him legally Dad for all purposes. While it won't change the child's name, it will mean that he can ask for, and may be given visitation or custody rights.