Can I still use a Green card which was stolen but retrieved?

You can use your green card. Yes, you need the green card to get a new social security card [if you have any use for such a card].

There is no law against you flying, however if law enforcement determines you are subject to a reinstatement of removal, they very well may...

I am on student visa , but my fianc'e got a green card if she sponsor me will my status gone to be changed or not ?

She can petition you if you get married. You can file to adjust your status when the visa is available, or not file if you choose not to do so. ...

Can I do anything regarding a determination of inadmissibility for immigration?

There is generally no one year of "punishment" so something is missing.

Permanent Resident wants to bring Spouce

I agree with the others, you will do it the normal way, by filing an I-130.

90 days. Make an infopass and explain your emergency.

Divorce

Possibly, there are quite a few different ways this process can go.

H1B: company placed in State A, I will work 80% of time from home in State B - possible?

There may be ways of doing it, but keep in mind the posting requirements and prevailing wage. You are looking for problems.

Difference in I 751 Waiver results between Infopass and USCIS Check Case Status

You should believe the infopass people.

Canadian citizen wanting to know if I can travel back and forth between Canada and US during spousal Sponsorship Process

After you file for adjustment, you can only leave the U.S. with advance parole.