Can this Hungarian sentence be read as the sort of general statement that would make including the "the" in an English translation optional?
Yes, for me it didn't require "the" in the sentence.
there are many houses in the large cities,What is wrong int this sentence,please?
Why is ház singular in this sentence? Why isn't it házak?
because "sok" is a "quantifier", as are numerals, and nouns after quantifiers are always singular, for example: "Sok ház" "Három ember" . . .