Learn Croatian: Buka je ovdje problem. - Noise is a problem here.

Just like the reflexive word se you are learning about in this lesson, the little word je (is) is an unstressed clitic. In Croatian, clitics almost always have to go in the second position of a sentence (the Wackernagel rule). That is why it must follow the first word, Buka.

Could I change the word order to start the sentence with Ovdje (here)?

Yes! You can absolutely say Ovdje je buka problem. Notice how the word order shifts, but because of the second-position rule for clitics, je just attaches itself right after the new first word to stay in that number two spot.

Why is there no word for "a" before problem?

Croatian doesn't use articles like "a", "an", or "the". The single word problem covers "problem", "a problem", or "the problem" naturally, depending entirely on the context of the sentence.

Are both Buka and problem in the nominative case here?

Yes, they are. Buka is the subject of the sentence, and problem describes what the subject is. When you use the verb biti (to be) to say that one thing is another thing, both nouns stay in their basic dictionary form (the nominative case).