Not sure about during period, but their sense of smell seems heightened during pregnancy. A big use of smell in nature is determining if food is safe to eat or not, and the threshold for 'safe to eat' is higher when pregnant.
Yeah I think its true, I can't smell for sh*t in general (busted up my nose when younger I guess) but the average girl can usually smell better then the average guy. They seem to be the first to smell a fart anyway :P
the reason why they need it is because the ones with less smell died;. men don't need to be concerned with trivial matters, we are the true survivors. we need them to have our babies.
In some studies I have read, They've said that women are around 40% more receptive to smell than men are. One of the reasons, at least in terms of mating, is that smell tells you about the immune system of the other person, so if you like how that person smells naturally, your immune systems are compatible.