Does my custody case move with me if I move out of the county?

Change of Venue is what you are looking for. Be careful as the history of your case and impressions of the judicial officer would also stay in the...

Alimony

Perhaps this may be as simple as filing and serving a wage assignment.

My X keeps posting "statuses" on Facebook regarding me and what a bad mother I am. Can I used this in court?

Absolutely. It is common now to include "no disparaging comments etc..... including social media".

Can I keep my new child if I lost custody of my two daughter's an now there adopted

Not unless there is an incident involving abuse/neglect etc. Hopefully the reasons for removal of your other two children have been resolved.

Can a person with an affidavit from a family member have the legal right to sell a family burial plot purchased by the parents?

Was the person identified that the plot was sold to? Any other family members around to inquire with that may shine more light on the situation?

Who pays attorney fees in contested Divorce CA

Attorney's Fees under FC 2030 depend on a need and ability to pay. Normally a disparity in income and savings are considered as sources to pay fees.

Will my ex's felony warrants in other states help me get custody of my son?

Depends on the nature of the warrants and whether they are extraditable or not.

I concur, no speedy divorce here in Ca. Now Nevada....

Am I violating a FAMILY court order?

If he never responded, keep record of that if he raises the issue with the court. You are trying to be reasonable and accommodate his phone call time.

Whose custodial time does the trip fall on? Why not both chaperone?