Learn Italian: Perché mangiano tardi?

Yes! In Italian, perché does double duty. Since it is at the beginning of a question here, it means "why". If you were answering this question, you would also start your answer with perché to mean "because".

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

Italian doesn't use helper verbs like "do" or "does" to ask questions. To say "do they eat", you simply use the verb mangiano and raise your voice at the end of the sentence to show it is a question.

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

Italian usually drops subject words like "I", "you", or "they". The ending of the verb already tells you who is doing the action. The -ano ending on mangiano specifically means "they eat", so adding the Italian word for they (loro) isn't necessary unless you want to emphasize it.

Why does perché have an accent mark on the last letter?

The accent mark tells you to stress the final syllable when you say it out loud. You put the emphasis on the second part of the word. Also, remember that the ch combination in Italian sounds like a hard English "k"!