If I drop the arbitration, will that be a failure to follow my administrative remedy?

I would continue the process until a decision is rendered in the arbitration.

Will my husband (after we are married) be able to write his name on the birth certificate without having to find the birth dad?

Unlikely. This isn't something you can address without court order now.

How do I get out of this contract and from the employer legally? My employer is CA and I work in MO, where does my case belong?

The contract likely has a jurisdiction provision. Read it carefully as it likely controls.

What action should she take, or where does she start- with the court that filed her paper with the forged signature?

If you resided at the premises the landlord may seek rent from you.

How do I go about getting sole legal and physical custody?

Unfortunately it is not your call to make. Hire counsel and file the appropriate pleadings.

Because there was no written agreement, is the verbal agreement legally enforceable or was the money given considered a gift?

You must repay the money. No intent to make a gift.

How long does it generally take to obtain Letters in an Estate Administration in Hillsboro County in this case?

Normal time period is two to four weeks after filing a request with the court.

Is it legal for a mortgage servicer to change the original loan agreement or any part of it without written notice?

Only your writing will help. Obtain a copy and read it carefully.

(1) Are private-project retainage arrangements freely governed by contract? (2) Can court remedies regarding retainage be waived

If there is not a prevailing wage or government involvement issue then two parties can agree to most anything they want.

There isn't a magic notice requirement to assign the interest. You should approach the new group either way to explore their interest.