I am american citizen born out of US. I would like to know what is the status of my mother - is she eligible for green card and how long does it take to get it. My mother is 72 and lives alone in my native country in Europe. I would like she to come and live in US with me not like a visitor but legal resident.

Yes, she is eligible for immigrant visa. It may take 12-20 months depending on the country where she comes from.