No. Well yes, and no. It is not recommended for newborn babies to be exposed to a large amount of sunlight. This is because a newborn baby's skin is so sensitive and thin that it is more prone to sunburn. The best thing is to keep your baby covered if you are in direct sunlight. Covering the baby with a stroller or a hat with a brim is best. It is ok to use sunscreen, but best to avoid the direct sun.
No. This is a tough one. Depends on how premature the baby is, and when you're taking them out. Generally after 6 mo you can use sunscreen. A very premature infant who is just going out for the first time probably should not be in direct sunlight, so a sunshade should be used. If not in direct sunlight, they don't need sunscreen. Check with your doc for exact recommendations.
Keep your. Newborn very covered! Avoid most sunscreens for 6 mos perhaps only exception pure zinc oxide.