Why is the carrier-pigeon so called?

Because of the service to which it was formerly applied, particularly in the Levant, of carrying letters.

It appears that as soon as young pigeons are hatched, a whitish ash-coloured fluid is secreted in their crop, both in the male and female, in abundance, with which they feed for some time the young before they feed them with grain ; so that, though pigeons' milk would be considered a solecism, yet this fluid seems to be very like milk in its properties. - Jennings.

Why are such numbers of London pigeons lost during the winter?

Because of the slight falcon, which takes up its abode every year, from October and November, until the spring, upon Westminster Abbey, and other churches in the metropolis.