With advance parole you can visit any country you wish and return to the U.S. There may be quarantine requirements lest you bring the dreaded...

If you are filing for DACA it should be no problem. Otherwise, it would be better to use your passport.

You may qualify for many different visas including U visas, E visas etc. Since you are not in status, you will need to leave the U.S. to get one...

If you are asking if a receipt for an I-485 authorizes you to work in the U.S., no, it does not.

Lawful permanent residents of the U.S. are not eligible for medicaid for five years.

It seems to me that the answer is yes if you filed with the National Visa Center to get your visa.

If someone filed an immigrant visa petition for you prior to April 30, 2001 and you have lived in the U.S. since December 20, '00, you may qualify...

Since you have not visited annually for the last eleven years, you have abandoned your resident status in the U.S.

Yes, a lawful permanent resident can file for her spouse to immigrate to the U.S.

It should be at the local USCIS. You can follow up with them.