1) My understanding, based partly on traditional lore and partly on my own experiences, is that it happens at quickening. Conception makes a first tentative connection between soul and body, but that link is often broken -- keep in mind that close to half of all conceptions result in very early miscarriage. The first breath outside the womb is the point at which the child has a fully independent energy body, and thus it's the crucial moment for the horoscope.

2) In earlier times the assumption was that you'd spend three times as long between incarnations as you spent in your most recent incarnation. I don't know of any discussion of the reincarnation timing of dogs and cats, but it's likely to be similar.