Yes. Get married. File I-130 (your petition for her immigration), I-485 (her green card application), I-765 (her work permit application), and...

The answer depends on whether you maintained your non-immigrant status all this time. If you did not, then you may not get F1 or work visa status.

Your asylum claim will be scrutinized for frivolity. Frivolous asylum filing bars any immigration benefit, including AOS.

This should have not gotten to this request, because it was clear as day that USCIS would ask for this proof. Engage an immigration attorney with...

Hire an experienced immigration attorney at once. USCIS took back your GC, because it gave it to you in error. Here is law that USCIS may do so...

Install the proper key board and type in whatever is their native language.

Too early for any such inquiries. Asylum is a gift - do not forget about it. If there was no legal brief in support off your asylum, submit one now.

Talk to your attorney about a possibility to expedite adjudication of your I-765.

Privet. Not a big problem. Get new translations in the transliteration matching her current spelling.

In the 9th Circuit, yes. Law is different across the U.S. Here is the map of federal circuits....