Can a H4 EAD holder live and work in a different state?

Yes, your spouse should have no issue with this new employment offer

How does USCIS know the my exact termination date?

The employer needs to inform of your termination date

Can I sponsor my father I just became us citizen but he has a deportation pending

There are many factors to consider such as when the deportation occurred, is the order final or is he currently in proceedings? You can petition...

H4 -EAD?

You can apply for your EAD to work if you are included in your husband's petition for adjustment of status.

Can my mom's uncle to support her to come to me in USA to visit?

Your uncle can't petition for your mom but she can bring evidence of his income and a letter of support when she reapplies for her visa.

F1 student, I-130 approved, is it time to file for Adjustment of Status? What if my EAD expires meanwhile?

You can file. You can only file AOS in the US if you are here in lawful status. Otherwise you have to consular process. You must renew your EAD to...

What should I do next?

It seems you never works with employer B. As such, you can focus solely on the I797 approval notice from your current employer A, valid until 2021.

You should definitely hire an attorney to assist you with this process. You can appeal the N400 decision or reapply but you need to be ready to...

K1 Visa in Administrative Processing?

You can always contact the embassy for updates yet they seldom give relevant information beyond "your case is pending."

Can I expedite EAD Application?

It appears your EAD is well within USCIS's processing times. As such, you will not be able to expedite it.