I applied the Adjustment of status got my wife the case is pending can she travel me inside USA by air?

Yes she can travel in the US but take a copy of the 485 receipt notice.

Since it is an extension it won't automatically get canceled but this would be a tremendous loss of money. By doing this you are essentially...

Unless there is something "bad" in your background like a conviction for certain offenses, membership in certain groups, violations of past...

Can I change my primary job from being a doctor to a forex trader since I have recently got my permanent resident card?

Assuming you have prior commitments to work in a specific geographical area, then you can essentially do what you wish to. Working as a doctor or...

I am an active duty airman I want to get married with my girlfriend but she’s Mexican what do I need to do?

You will have to wait for February to marry or get her parents' consent to marry. A lot of the timing and document issues depends on where she is...

You are fine. The receipt notice will extend your CPR for 12 or 18 months.

Can I re-enter the United States after leaving one year while having a Pending Asylum Case?

Your asylum case ended when you left the US.

How do I get permanent residency card in US and how long will it be??

If you are in J-1 status you will need to enter an underserved area program to get H-1 status after your residency.

Can I accept an offer for remote position on H1-B or F1 STEM? Should I wait for H1-B approval or withdraw and start a new one?

You cannot file for new H-1 until your current case is approved.

This is a question for your immigration attorney to answer.