Check with your doctor before you play in hot weather. My wife insists I wear a hat if I'm playing on a hot day. But I look terrible in hats. Make sure they are wide-brimmed to offer the most protection. If you insist on putting fashion before function, baseball-style caps are all right.
Any hat is better than no hat.
Yes, as a matter of fact, they do. Bolle, Oakley, and Ray-Ban produce sunglasses for golfers that keep out nearly 100 percent of the UVA and UVB rays that doctors say are dangerous both to our eyes and skin. Besides the health benefits, the companies have developed lenses that allow you to read the subtle breaks in greens, which you can't do with regular sunglasses. But I wear prescription glasses. Yes, some of the companies above can make prescription lenses for their wrap-around frames.