Does sunscreen expire?

Yes. Sunscreens have a shelf life of three years. After this, they start to lose their stability and efficacy. You should see an expiration date on your bottle of sunscreen and should use it before that date. If you don't see an expiration date, write the month and year you purchased it on the bottle and toss after three years. Do not use any sunscreen that has become lumpy or has turned an odd color.
Yes but block better. Sunscreens may deteriorate whereas sunblocks tend to be physical barriers that withstand longer periods of storage.
It can. All products with a shelf life have an expiry stamped on the bottle.
Yes. Yes sunscreen can expire. Especially the ingredients that protect you from the uvb rays (the cancer-causing rays). Things like zinc or titianium oxide protect against uva (aging rays) and last longer. You should buy new sunscreen every season. Better yet, you should be using it up so frequently that it never has a chance to go out of date! protect yourself.