You have to go to Juarez for the interview OR ask for rescheduling. You cannot process in the US.

You cannot work without authorization.

Is this normal?

There's a backlog in the Houston office. You'd have to wait a few more months for an interview.

Yes, depending on his immigration status. Have his criminal attorney work closely with an experienced immigration attorney.

How can I sponsor myself for a Green Card ? I have a PhD from a well known university in USA

a PhD alone doesn't qualify you. If you have experience, publications, references, etc. you may qualify for EB1a. Consult with an experienced...

Can officers issue citations for reckless driving after they let me go with a verbal warning ?

If you did not receive a ticket, you should be fine. However, you can always check with your local court database to ensure there is no citation.

Immigration question

This is possible but very difficult. Consult with an experienced immigration attorney.

Not likely. How did you get the temporary driver's license? It is advisable to privately consult with an experienced immigration attorney.

Do we need to file the waiver or re-apply for a K1 visa?

The best route is to get married and file an I-130 Petition for Alien Relative. You should consult privately with an experienced immigration lawyer...

I’m on 10 years deferred probation I got a ticket for no license will I get locked up ?

I doubt it. However, discuss this with your probation officer asap.