"What do you want?"
Translation:Bạn muốn cái gì?
Is it more common in daily speech to omit the cái? Also, the pronoun? Do people just say: Muốn gì?
It is natural to say "Bạn muốn gì." But "Bạn muốn cái gì" is also acceptable if you want to emphasize your point. However, "muốn gì" is considered rude. You should never take out pronouns unless you're talking to your CLOSE friends. Even then you need to be sensible with it.
Would it be incorrect to use "chiếc" here instead of cái? If so, why is that?
Chiếc and cái are the same, but what is cái gì, we (native speakers) never said chiếc gì. Chiếc gì is used in this situation and it is not only mean what You: Mẹ ơi, con mất một chiếc vớ rồi (Mom, I lose a sock) Mom: Chiếc gì? (Which sock? ) You: Chiếc/Cái vớ màu đỏ sọc trắng (the red sock with white stripe)