Will it harm our case if I travel to Mexico to visit the wife for the winter while our I-130 is pending?

Preparing for the 601 if that is really necessary. Find a cosponsor if your income due to the trip will cause you to fall below 150% of the poverty...

I-130 Case status states; "case cannot be found" Is this typical?

Not typical, but not unheard of. Call the 1-800 number at the bottom of your notice of action.

Do I need to renew my Green Card if I am a U.S. Citizen through my father becoming a naturalized U.S. Citizen?

Not if you are a US citizen.

If a petitioner for a spouse has had an arrest on the record?

Not likely to come up, but it could. I have seen officers inquire as to the USCs criminal history in order to ascertain the extent to which the...

My I-94 wasn't taken by the USCIS Officer during and after my AOS interview,

Is yr wife a USC? Did you have an attorney present? As my colleague states, your fact pattern is slightly confusing.

My kids and I got a tourist visa to the USA, I am a medical doctor, our nationality is Iraqy, I want to apply for Asylum

None of us are likely to tell you what you should or should not do other than to contact an immigration attorney. That said, your matter is serious...

I am personally rather fond of prenuptial agreements when it comes to evidence, particularly in cases like yours. The reason is he is both wealthy...

Does USCIS waive interview after satisfied with RFE submitted

Depends on what basis the 485 was filed.

How long does it take to get a receipt back if I file a form I-90?

Between 7 and 9 days.

Is there a fee for the DS 230 form?

Form DS230 is no longer in use.