Yes, and tradition. A woman can get hired to work at a bank with pierced ears, but probably not with a pierced nose. There's nothing in the Handbook of Chemistry and Physics that says one is more acceptable than the other, though. It's purely cultural.
That difference will be gone in ten years if it isn't already, although oldsters will continue to bemoan it for another twenty.
Well, yes. The fact that if you walk around with only a t-shirt covering the upper half of your body then people say nothing whereas if you walk around with only a pair of underpants covering the lower half of your body then people say "ugh, good god, put some fucking pants on, dude!"
This is not a random arbitrary social choice, either; if you're showing your underpants then you're not far away from showing other stuff we really don't wanna see. That's why the social convention is that you need two layers downstairs and one layer upstairs to be considered dressed.
If your next question is "yes, but why do people object to seeing strangers' genitals?" then I could point you at some ev-psych just-so stories, but the answer is "we just do, okay?"
Of course it is. Tee-shirts are now conventional and perfectly acceptable outerwear in most circumstances. Underpants aren't.