Technically everything moves at c (the speed of light) through spacetime, all the time. Most objects that have mass spend the majority of their motion in the time part, and thus move relatively slowly in space. If an object moves fast in space (where fast is a significant fraction of c) then it moves noticeably slower in time because the total spacetime vector value is always c.
Photons, being massless, do not move through time at all, and move through space at c.
At conception, yes, there is no sexual differentiation. In humans the SRY protein is responsible for a fetus developing male sexual characteristics. The effects of this gene are expressed after week 6 of development:
That is, at least a month and a half after conception.