Is negative HBsAg hepatitis b test conclusive 14 weeks after exposure in a healthy adult?

Quite conclusive. HBsAg is the first serologic marker that can be detected following exposure to HBV, as early as 1 or 2 weeks and as late as 11 or 12 weeks post exposure. If you are 14 weeks post exposure, it should be quite a convincing that you did not acquire an acute hep B infection. You should still discuss with your doctor regarding his thoughts on this. .
Yes. The false negative rate is pretty low from what I remember. You should be ok.