I am a little surprised that so many Greek words for clothing are of foreign origin (e.g. φούστα, (που)κάμισο, παντελόνι and καπέλο are loanwords from Italian; παλτό, μπουφάν, μπλούζα and κασκόλ are from French; ρούχο is borrowed from Bulgarian; παπούτσι from Turkish; etc). What happened with the native Greek vocabulary for clothes? Definitely the Ancient Greeks were dressed with something, presumably shirts, pants and shoes... Did their clothing go out of fashion and hence the terms for it were forgotten or what?
Ancient Greeks wore tunics (χιτώνας), sandals (σανδάλια) and cloaks (μανδύας). Shoes in Greek are υποδήματα (also used in Modern Greek, just not so common as παπούτσια). Ρούχο is also ένδυμα (which is also used). It is just as you said, though. Ancient clothes are not worn nowadays, except for the sandals.
Isn't φούστα a blouse? In 2 examples before " I am wearing my blouse": "εγώ φοράωμια φούστα" and "the blouse": "η φούστα" it was presented as a blouse. Suddenly, in this exercise, there was no "blouse" option. The answer was skirt. Well, now I researched and Google translate gave me "blouse" : γηλούζα."