Ubrania is nominative=accusative=vocative ubrań is genitive.
Nominative is subject, accusative is direct object of most verbs, genitive is possession, direct object of some verbs, and direct object of most negations. Accusative and genitive also sometimes appear after certain prepositions.
Generally yes. It's a bit more like "clothing", I imagine.
For example, a shop with clothes will rather be "Sklep odzieżowy", but to say "moja odzież" (it's feminine, remember!) instead of "moje ubrania" would feel very strange to me.
"Rzeczy" are often used for clothes, if the context makes it clear, but I don't think it should be accepted - it's a colloquial usage anyway. Removed the answer.
"ciuchy" are also colloquial.