Welcome to the Wefugees Community and thanks for sharing your questions with us!
About your permanent residence/Green Card for USA: I am not an expert on US-immigration regulations, but I made some research and learned, that you may lose the lawful residence permit (LRP) if you are
- Moving to another country with the intention of living there permanently (some sources say that you will lose it if you are living outside of the US for more that 12 months);
- Failing to file income tax returns while living outside of the US for any period of time;
- Declaring oneself a 'nonimmigrant' on one's US tax returns.
Please check, for example, this website for more details.
Regarding your potential return to Europe: I am not 100 percent sure, if every country deals with it in the same way. But as I know from Germany, people usually decide to get support for a "voluntary" return to their country of origin to avoid a ban to re-enter the country. However, I also read, that IOM may ask for a repayment of the money if you decide to come back (depending on your reason etc.).
I hope this will answer your questions. In any case, please feel free to get back to us if you want to discuss your situation further.
All the best,