Dear @Concerned,
Welcome to the our community and thank you for sharing your story. I’m a not a clinician and so am not trained to provide medical advice. But as a scientist, I can provide some background on the virus biology and lab results.
Regarding your lab results, they indicate that you have been previously exposed to Hepatitis B (because you are positive for Hep B core antibody) but that you have cleared it (because you are negative for Hep B surface antigen). This would be the outcome of an acute infection or clearance of a chronic infection, which is a great thing and is what many of us here hope for.
Regarding your risk for transmission, it is extremely low. Your DNA levels are barely detectable. Others here have had much higher levels (1000s IU/mL) without knowing and not transmitted to their partners (e.g. Partner is not positive for HBsAg, anti-HBs, or anti-HBc).
Hope this helps and relieves some of your fears.
Thomas