Learn Croatian: Vi ne razumijete problem. - You do not understand the problem.

No, Croatian does not use helper verbs like "do" for simple negation. To make a verb negative in the present tense, you just put the word ne directly in front of it. So, "you understand" is razumijete, and "you do not understand" is simply ne razumijete.

Do I have to include the pronoun vi at the beginning of the sentence?

You do not have to! In Croatian, the ending of the verb (-te in razumijete) already tells us that the subject is "you" (plural or formal). You could just say Ne razumijete problem. Including vi makes it a bit more emphatic, like saying "YOU do not understand the problem."

Does vi mean "you" as a group, or the formal "you" for one person here?

It could be either! The pronoun vi and its matching verb form razumijete are used for both a group of people ("you all") and for a single person you are addressing formally to show respect. You would rely on the context of the conversation to know which one it is.

Why does the word problem not have a special ending here, since it is the object of the sentence?

Because it is the direct object (the thing not being understood), it is in the accusative case. However, for masculine nouns that are non-living (inanimate) like problem, the accusative form is exactly the same as the base dictionary form. So, its ending does not change!