Can I adjust status to GC based on EB-1 or EB-2 NIW from pending asylum filed on valid status?

I agree with my colleague. You may have the additional problem that pending asylum is not a status and if it is the basis for your remaining in the...

Can I travel outside of US with expire green card and I-797C receipt notice?

Your status as an LPR has not expired even though the card has. However, You may not be admitted back into the USA with an expired green card...

You may travel with the stamp in your passport provided it is not expired. Whether you may travel while on "informal probation" I don't know...

Can I sue my previous employer because I was returned back from USA airport when travelling on B1 Visa?

Sounds like your employer told the truth and you misrepresented yourself.

Form DS 260 immigration document

You will receive a request for evidence and it will delay the processing fo your case if you do not file it with your original application.

Regardless of age an LPR needs a re entry permit if ou plan to be out of the country more than 6 months. Even with the re entry permit it is...

Can my under 18 kids fly within the US with only a sate ID and with a green card pending??

The airline only requires a photo Id to board the plane. For immigration purposes there is always a risk when you travel while out of status....

Charged with aggravated felony and deported

Pursuant to the Immigraton and Nationality Act a convicted aggravated felon is banned from the USA permanently.

What should we expect?

Your situation is very specific to your circumstances. I suggest you consult with an experienced immigration attorney.

Submitted marriage license & put a different location for the marriage location...will this affect wife's green card process?

It is best to put the actual address. If the interviewing officer looks closely at the location and photos you provide it could raise questions.