Your post seems all over the place but I understand your stress level.
I traveled to my COP and renewed my national passport. I had the passport with me during the interview (in Baltimore MD) and never intended to hide anything. The officer used it for identification purposes only and had no interest in discussing it further. I am NOT advocating this was a good thing to do. What I am saying is don't panic. It is too late to change the past. Focus on your test and other things you have control over.
I do not know the particulars of your case. My personal asylum claim never suggested that the COP government would execute me if I set foot there. What I established is a "reasonable fear of persecution on account political opinion" and this remains true to this day. I had a solid reason to visit and stayed a very limited amount of time (8 days or so, not sure).
Also remember that you are a PERMANENT RESIDENT, not an asylee. Circumstances in you COP may have changed. This does not mean that your asylum application was unfounded. I see too many people on here scaring the hell out of others and I find it ridiculous.
File your FIOA and get the information you need. There is zero reason to worry about this.