It depends. How long have you been working for this employer? What is the reason for the change? Etc.

How can we fix the situation where we haven't reported employer information for F1 OPT EAD in time?

You need to speak with an attorney. She might have to go for visa stamping.

Passport expired

I think you should talk to 1. consulate of your country; 2. an Immigration attorney to explain where you are going to travel. If it travel by air...

6 year completion

It may be PERM or it may be 140. Speak with your lawyer.

Can I use my remaining OPT (F1)?

Did you join that university for a higher degree? What happened with your employment? You need to speak with your DSO.

Parole in place

The instructions to the form I 864 explains what amounts you need to take into consideration. After parole in place you can file for AOS, or...

What to do if I want to travel to France but I don't have a job (letter from employer?) as visa requirement?

It is a good question, but for lawyers who practice French law.

People with mental disability falls as particular social group for political asylum? even from Brazil?

Maybe, depending on specific circumstances.

Can my sister who is a Us citizen apply for my green card?

She can, but it will take about 10 years or so, and you still probably will have to get some sort of a waiver.

Haitian Family Reunification Program? Immigrant Visa Issue?

Perhaps, he got into the maze of an administrative processing. All you can do is to follow up.