I know the answer shows "цей суп з морквою" but I think "це суп з морквою" should also fit, because in English you can be talking about a specific soup (цей) or pointing at something which you think might be soup. As in: "Що це? Це суп з морквою?"
Shouldn't carrots be морквами instead of моркваю since it's plural?
This sentence sounds unnatural in English (American English, at least). The natural way to ask this question would be "Does this soup have carrots?" or "Are there carrots in this soup?"