Are white cats vulnerable to sunburn?

Yes. Their eyes and nose pad are vulnerable. Their body is covered by fur so they won't get skin cancer or sunburn. A hairless cat would be vulnerable to sunburn. The nose pad, if it is pink, will lack the dark pigment that protects it from sunburn and cancer. That is why animals that have nose pads (e.g. dogs, bears and cows) generally have dark nose pads. If the eyes are blue, then they do not have any dark pigment, and eye cancer is more likely than cats that have eyes that are green, yellow or brown.

No more than any other color of cat. Hairless cats are.

Yes, although they would reflect more sunlight than black cats. Cat's ears are particularly vulnerable to sun damage where they can't find shade.