"The old lady is wearing a nice dress."
Translation:Den gamla damen har på sig en fin klänning.
So, "an old lady" would be "en gammal dam", the indefinite form, and "gamla" is used in the definite and/or plual forms (the lady/ladies)?
How do you differentiate between "gammal" and "äldre"? I have heard that it is rude to refer to old people as gammal, and that "äldre" would be more polite. In this case, it is not allowed. Is that because we are translating "old" literally?
In this case, it's more that äldre doesn't work that well attributively with the determinate form. Den äldre damen har på sig en klänning – I would interpret that as literally comparative (she is older than some other person previously mentioned).
About the general difference between gammal and äldre, that's a bit complex and I hope someone else will step in and provide an explanation of that, I just wanted to weigh in on this specific sentence.
lady means dam, so since the hint is on the word dam, that's how it will have to be.