Translation:A young woman was looking at the dress.
At first I wrote 'The young lady was looking at the dress' which was marked incorrect. To me as a native English speaker this sounds much better and (I believe) this would probably be the phrase used by the majority of English speakers. Is the word 'kobieta' used solely for 'Woman' and if so is there another word used for 'lady' ?
Yes, usually "kobieta" is used only for "woman". The translation of the word "lady" can be either "pani" ("ladies and gentlemen" = "panie i panowie") or "dama" (in films "young lady" is often translated to "młoda dama").