Of course they can. Many kids have congenital myopia or other eye problem so that they must wear glasses. But usually it is too hard to test them before age 3 or 4. The best way is to talk with your eye doctor.
Sure. Sunglasses will help prevent your baby's eyes from UV rays which is very harmful to the eyes. If your baby loves wearing sunglasses, then you'd better pick a pair of sunglasses that should have 100% UV protection for your baby. Don't choose the sunglasses with poor quality, it will damage your baby's eyes. If your baby doesn't like wearing sunglasses, a hat with a brim is also a good choice to protect the eyes.
I think baby should be exposed to sunlight but it doesn't mean we can put a baby directly under the sunlight. Sweetie, you can take your baby out when it is warm in the outside. If it is hot in the outside, I think you can't take your baby out. My aunt used to play with my little brother in the balcony when the sun just rises in the morning. The sunlight will not hurt his eyes at that moment.
Baby can wear sunglasses. But if you make the baby to wear your sunglasses, I think it is not a good idea. Usually baby has a small head so your sunglasses are not fit for him or her. If your sunglasses are prescription glasses, you can't let your baby wear it. Your baby is just 4 months. you can't take him or her out often. Once I saw my brother frown and closed his eyes tightly when I took him out. And my mum told me that the harsh sunlight made it hard to open his eyes and will also damage his eyes. So usually mum would give him a hat to protect his eyes when took him out.
Babies can wear sunglasses. Sunglasses can shield their eyes from strong UV rays of the sun. But it is quite difficult to ask a baby to wear a pair of sunglasses. Sometimes they will be hurt by the hard frame because they want to play with it rather than wear them to protect their eyes. I think you'd better buy a wide brim hat for him.
I think baby's skin is very tender. Too much exposure to sunlight may burn the skin. And the glare sunlight will cause damage to his or her eyes too. So I think you'd better not to take your baby out to enjoy the sunshine at this moment. You can take him or her out when they get older (maybe six months). You can buy him or her a pair of sunglasses at that moment and he or she may understand that the sunglasses can be used to protect the eyes.