Yes you can if you want to! Although most wont need one for the first few days! They come in different sizes 0-3 months and so on!
Not if u r breastfeeding, that has to be established first.
i recommend you don't do it when you're breastfeeding because then she'll be confused and not know how to feed! that's what happened to me the nurse gave her a pacifier when i was breastfeeeding her and it broke my heart that she didn't know how to feed from me anymore and they tried showing me techniques to express my milk to her but it was just so hard and frustrating!!
but if you're not then completely ignore what i just explained lol
You could but are you breastfeeding? as it can cause nipple confusion and mask hunger cues.