What to do with abbreviated middle name

You should use the spelling in his birth certificate.

Uh, probably not. Travel around the US, might be. Consult with an attorney.

Would my wife be denied entry with an approved advance parole?

She should not be denied entry if she travels using AP, unless she is inadmissible on some other grounds.

Can I earn $ teaching tennis as an independent contractor at venues other than my sponsoring club with a P1 visa?

You cannot in most cases. Were you sponsored by your employer or an agent? You cannot be self-employed directly in P status. You should consult...

What are the ramifications if my contract with the petitioner/sponsor is terminated before my current visa expires.

You will have to leave the country, unless, of course, before this happens you file for change of status/extension, etc.

Can i travel inside n outside USA while having F1 student visa?

Speak with your DSO, it should not be a problem, as long as DSO signs permission and you have a valid visa.

What are my chances to have a student visa F1 or H1B rejected after this situation? What may my further actions be?

What was the reason for the denial? I am afraid it will be difficult to get a non-immigrant visa after this.

How do we apply for a STEM Extension for a Non-Everify company?

The employer will have to become a E-verify employer. Many employers do not want that, because it comes with certain obligations and possible audit...

You can join employer B after B files for you. I think you should consult an attorney in person.

May I file Affidavit of Support (I-864) concurrently or I should wait till NVC mails this form to me to complete?

If your parents are outside of the US, you will be filing I 864 after the I 130 is approved. If your parents are in the US, you will file the whole...