Learn Croatian: Nemamo problem. - We do not have a problem.

The verb imati (to have) is a special exception in Croatian. Instead of just putting ne in front of it, it merges with ne to form a completely new negative verb: nemati. For "we", it conjugates as nemamo.

Where is the word for "we" in this sentence?

Croatian usually drops the subject pronoun, like mi (we), because the verb itself tells you who is doing the action. The -mo ending on nemamo already means "we do not have".

The verb "to have" usually forces the next word into the accusative (object) case. Why hasn't the word problem changed its ending here?

It actually is in the accusative case! However, problem is a masculine noun that represents an inanimate object (not a living being). In Croatian, masculine inanimate nouns look exactly the same in the accusative case as they do in their basic dictionary form.

Why isn't there a word for "a" in front of problem?

Croatian doesn't have articles like "a", "an", or "the". A noun like problem just means "a problem", "the problem", or "problem" on its own, depending on what makes sense in the English translation.