Upvote:2
However, I would like to know if I can travel to places like Europe.
You should have no problem traveling to Europe on your unexpired valid passport after acquiring a visa (if required of Korean citizens), provided it has not been revoked by the South Korean government, which is unlikely
Is it possible for me to get a European visa (as a Korean and a US permanent resident) in any other means?
Yes, see above. You do not have to go to Korea to apply for a visa to European countries. Finally, long term travel/migration and applying for work permits etc is beyond the scope of this part of stack exchange. You can check expatriates.
Upvote:2
My understanding is that as a south korean you do not need a visa to visit Europe. If you were still in F1 status then getting a visa to get back into the US may be a problem, but as a US permanent resident your green card suffices to re-enter the US.
Generally requirements for where you can get a visa depend on residency not citizenship. So it should be no problem to apply for a Visa as a permanent resident of the US if/when you need one.
Regarding getting a job AIUI it is normal to attend job interviews (with companies/institutions that are licensed to sponsor foreign workers) as a visitor, but then it is normal to leave the country while the company makes it's descision and then the process for your long term visa/residence permit/work permit is dealt with. The UK outright requires leaving the UK for this process, i'm not sure about other countries.
(personally if I were you though I would try to stay living in the US until you can get US citizenship)