I am nit sure how they could?
They usually ask if it was miscarriage or abortion. I'm sure they can tell if they actually ran test but the doctors are on ur side so they don't suspect u would lie. Its ur choice but I would tell them so they know.
What exactly do you mean? Are you asking if your ob will know if you had a planned termination or a natural miscarriage?
It all depends on how long ago this occurred. If its been over 3-4 weeks then there's no way to tell since the uterine lining should have rebuilt itself at this point. Either way you should notify your ob of any previous pregnancies as it matters for your overall medical and reproductive history.
Probably something you should let your OB know anyway...