To some degree, yes. There are fabrics specifically designed to have higher protection from the sun, and multiple layers are much more effective at preventing sunburn. However, typical clothing is fairly loosely woven and so some sun does get through the weave.
There are swim suits specifically designed to be tanned through, for those who don’t want tan lines but don’t have the privacy (or chutz pah) to sunbathe in the nude. You can find some here and here and here.
I’m sure it’s possible, though I never have. I burn like a true Irishwoman, but not through clothing. I guess if you’re outdoors long enough… also, I’m sure if it’s intensely hot outside it can redden your skin. Well, my white ass anyway.
Must be, since they now sell clothes that prevent the sun from burning you—so the ones that are not so treated must allow some light in. It would be likely that the thinner and lighter the clothes, the easier to burn through.
Absolutely! I decided to re-shingle my roof myself. I spent many days on the roof wearing blue jeans, t-shirt, and ball cap. I got a very bad sunburn through my shirt and a moderate sunburn through my hat. It came as a complete surprise but I covered myself in sun screen after that . A sunburned head is especially uncomfortable because it itches and burns at the same time.