I am not a doctor. You asked some interesting questions, I will reply with my opinions, not necessary correct.
In the serological test for HBsAb, some labs will just report positive(reactive) or negative(non-reactive). But some labs will report with a quantity, e.g., x IU/L. If x is less than 10 iu/l, the labs mayl comment "negative" or "non-protective".
In general, my opinion is that HBsAb, whether it is "positive" or "x iu/l" is not important AS LONG AS HBsAg is positive. The reason is that even though you have s-antibodies, they are not the right types for your s-antigen. Why do you have these variant types of s-antibodies is a moot point in the scientific circle.
There is no sure way to find out how long you have been infected. Vertical transmission is the first thing to consider. However, you did say your parents tested HBsAg negative, but was your Mum infected in the past and since then had recovered? One way to check is to test your Mum's HBcAb. Or did you have any medical procedures in the past?
The fact that BCP(Basal Core Promotor) mutation is detected, may or may not indicate how long you had been infected, but in my opinion, it is most likely have to do with the fact that your are HBeAg negative. The theory is that HBeAg seroconversion always involve some mutations in precore/BCP that lead to reduction of serum HBeAg (another contentious issue).
Finally, you do not require treatment now. But if you do consider treatment, please consider PegIFN as you are genotype A and female, very favorable factors for a cure with PegIFN. Check with your doctor.(no PegIFN at least 6 months before falling pregnant).
while I was at the dr. office last month, the dr. also told me there was a case where one of the patient got the hbsab, then lost HBsAB 6 months later. normally if HBV DNA is undetectable, HBsAG non-reactive, and HBSAB reactive at the same time, then it is a very good indication the immune system is responding and should be able to suppress hbv on its own, and produce HB surface anti-body for life.