Yes. Absolutely. Babies need this kind of so called non-nutritive sucking as a way to self console. They need to be able to breathe through their little noses so if they have nasal obstruction, as from a cold, it could make it hard with a pacifier in place. In this case, talk to your doc about salt water nose drops.
Yes. Although it may fall out, and the first few months they may cry until you put it back in (cause they can't find it), it is safe. There is even data suggesting it reduces crib death risk.