For what it's worth, as a native (US) English speaker, I don't think there's anything at all wrong with the English translation "a lot of sugar," whether it's used as a question or as a statement. The only way I'd expect to hear "much sugar" used in English would be in a phrase like "too much sugar" or "how much sugar." (YMMV.)
I (native AmE) feel a slight difference between "a lot of sugar" and "plenty of sugar."
To my ear, the first is a simple statement of quantity, while the second feels more like a statement of quantity relative to some unspecified standard or need. So, to me, "we have plenty of sugar" says not only that we have a lot of sugar, but also that we may have even more than we need for some specific purpose (like baking six trays of yummy brownies for the picnic...)
I don't have any problem with accepting "plenty of" if it works for the Czech natives on the team. But I do think it sounds better in a declarative statement than in a question, unless the question is just repeating what someone else has said -- A: "Do we have enough sugar?" B: "We have plenty of sugar!" A: "Plenty of sugar?"
Looking at it from your point of view, "hodně cukru" is also not a proper Czech sentence - with predicate and subject. It only determines the amount of sugar.
"hodně cukru" translates as "a lot of sugar"
How much sugar do you put in a cake? A lot of sugar. - Kolik cukru dáváš do dortu? Hodně cukru.
Thanks for the downvote.
You said it is a frequent question, so you'd better use it in your example. ;-)
"A: How much sugar do you want? Kolik cukru chceš? - B: Three spoons/cubes. Tři lžičky/kostky."
I'll add one situation where I'd use it as a question: "A: How much sugar do you want? Kolik cukru chceš? - B: A lot of sugar. Hodně cukru. - A: A lot of sugar? Hodně cukru?"