"Do you want some sugar?"
Translation:Volete dello zucchero?
Yes, these prepositions are pretty tricky considering that sometimes di and da translate into the same word in English :)
Dello is a partitive (indicates a rough quantity) which is di (primarily meaning of) + lo (the article for a masculine noun beginning with z). You can pretend di+article means of the as a possessive, and some as a partitive.
- La torta del (di + il) ragazzo/The cake of the boy/The boy's cake
- Il ragazzo mangia del (di + il) pane/The boy eats bread/The boy eats some bread
Dallo is not a partitive. It is da (primarily meaning from) + lo. As such, da+article will usually mean from the.
- La torta dal (di + il) ristorante/The cake from the restaurant
- Il libro dalla (da + la) donna/The book from the woman
In english you can not tell "you" the singular version from "you" the plural version by looking at the word "you" in isolation. In this case, as you noted, the options do not include "volete" (plural version), only "vuoi" (singular version) so it must be the singular version of "you" that is meant.
Qualche and alcuni translate to some when the noun is countable. Sugar isn't really countable.
I know what some of you might say... your favorite drive through coffee spot doesn't correct your English when you ask for a medium coffee with four sugars ;) Well, it will be difficult to find coffee like that in Italy, and you may also want to note that the sentence here asks for the translation of some sugar, an indefinite amount of a mass noun.
Hope that clears it up a bit!
"Un po' dello zucchero" means "some of the sugar", which only makes sense when talking about some very specific sugar, e.g. if someone was holding sugar and sweetener and you asked for the sugar. "Dello" alone has a meaning of quantity as a partitive article, but you can stress it with "un po' di": you can't mix the two, as soon as "dello" isn't alone it's no longer an article. It's either "un po' di zucchero" or "dello zucchero".