Is énekesfüggönyökről, like, an actual word? Apparently I was supposed to know that it would make for a correct sentence.
You mean "énekesfüggönyökről" as one word? No, it should be two separate words. But that is just because singing curtains have not been invented yet, as far as I know.
Why must "énekel" come at the end of the sentence (as opposed to " a furcsa énekesnő énekel függönyökről és szőnyegekről")?
Duo's preferred translation has the most neutral word order. Yours is correct too (so I recommend reporting it if it wasn't accepted), but it emphasises énekesnő: she's the one who sings about this stuff and not someone else.