She seemed embarrassed to go barefoot and to be watched when she took her boots and gloves off. Since we can see when she is wearing those pieces of clothing does this mean she is constantly walking around naked?
I think she is. Even tho what Zach said might be true (and as for her gloves and boots, it might be for her allies to see her) when she get her winter uniforme (in chapiter 194) she says that she's freezing when Kyoko ask her if she is cold. (so UA could probably have Make a warm one) And for what Gorzius said, she doesn't have to be naked to make him a pervert for bumping into some parts
I assume that with the technology disposable at UA they can manufacture something similar to Violet's suit from the Incredibles. It's not the suit that can turn someone invisible, but the person's powers that turn the suit invisible. The suit turns invisible with the person's powers (so for Toru, because she can't turn her powers off just yet it would be activated once she put it on) So along with Class A's costumes, Toru got hers which is a one piece suit. I assume and the gloves and boots are her own, which would explain why she needed to take them off. As for the logistics I think UA would have considered light refraction or something like that as we can see she figures out she can manipulate that too 🤔
Yes I do think that Toru Hagakure is always naked because in season 1 episode 5-6-7 while they were taking the test with All Might, when she came with her partner she was taking of her boots and gloves and then her partner had thought,"I can't believe there is a naked girl standing right next to me". Plus we have never seen toru in human form.