First, the original discharge sounds like it was nothing - assuming there was no odor, itching, or burning. Sometimes, if there is a small amount of bleeding in the early pregnancy
(which is normal) then it can make its way out as a brownish discharge.
The white discharge sounds normal as well. There is an increased discharge with pregnancy. If it becomes symptomatice - itching, burning, or odor - then contact your doctor for treatment.
With regard to the fetus, it is totally protected from what is going on in the vagina!
I hope this helps!