Marriage while spouse's asylum case is pending

Consult with an immigration attorney before your tourist visa expires to see options. Unfortunately just because you marry her, USCIS doesn't have...

How will someone be able to study in temporary protected status?

Yes, you can stupid while on TPS. Discuss your status with the foreign advisor at the school.

Does filing a motion to reopen with DOJ mean I can have USCIS reopen my I-485 now that I have received I-130 approval?

Once the court terminates your case, you can reopen or refile your adjustment of status with USCIS. Consult and retain an immigration attorney to...

Is it risky to hire a lawyer who has only been practicing for a couple years?

You have to do your research and hire an attorney you are comfortable with. Just because she has only been practicing for 2 years does not mean she...

Which department should I go to go home ?

Immigration will not stop you from leaving the U.S. You can simply fly home, no need to report to ICE.

I need attorney to become a legal resident of USA?

You might be eligible for a provisional waiver. Consult and retain an immigration attorney to help you legalize your status.

It seems unlikely, since she was denied 5 other times. I am assuming she got denied for immigrant intent. Consult with an immigration attorney, but...

Which date should we reference for the filing date for i-485 per visa bulletin: final action dates...or dates for filing...?

You should go by the priority date (date I-130 filed).

Can a US citizen get in trouble for this with immigration ?

Yes, an immigration attorney will never advise you to commit fraud on any government paperwork.

Birth citizenship ?

Yes, he or she will be a USC. And congratulations!