What does these mean? negative hepatitis b, core antibody hep b core ab, tot reactive hepatitis b, surface antibody?

Your statement is not clear. You probably mean: negative Hepatitis B core antibody and total reactive Hepatitis B surface antibody. If what I say is correct, you have vaccination for Hepatitis B in the past (most of Americans at you age have been vaccinated with Hep B vaccine in childhood) and you were never infected with Hepatitis B. I hope total reactive means Ab titer is above 10.