I’m going to Czech Republic embassy for visa request interview in New York. Now I’m filling Visa application online and don’t know what should I put on question #7 Current nationality. Nationality at birth, if different. As I’m asylee and have Refugee Travel Document (no Green Card, yet) what should I put?
The question is about your nationality, not your travel documents. Getting refugee status, or residence (a green card), doesn’t change your nationality. You should answer with whatever citizenship you have now, and had at birth if you have subsequently changed citizenship.