First, let me explain my background. I came to the USA on a tourist visa 18 years ago from South Korea and have never been out since. Thus my USA visa has long since expired, but I changed my status to F-1 (note the subtle difference between F-1 'status' holder and F-1 'visa' holder. I did not have an F-1 visa). However, I have recently received a green card.
I am now into my fifth year of Ph.D. and will apply for postdoctoral academic job positions.
Here are some questions:
1) If I travel outside the US, now re-entry to the US would not be a problem since I have obtained a green card? I won't travel to Korea, since I did not serve in Korea's mandatory military service; therefore, they probably won't let me leave again (especially since I have left the country with a tourist visa and never returned). However, I would like to know if I can travel to places like Europe.
2) I would like to have options to apply to some jobs in Europe. However, for the reason I explained above, I am unable to get a visa directly from South Korea. Is it possible for me to get a European visa (as a Korean and a US permanent resident) in any other means? Maybe I can enter a European country, and change my 'status' there to some valid legal status without obtaining a visa? (Just as I did in the US with F-1 status)
EDIT - I do have a valid South Korean passport, which expires in about 8 years or so.