You can end a sentence with "~합니다" unless you make a question. "~합니까" is asking. And now I can see where you felt strange about "~이에요" Unlike "합니다/합니까?", you can use "~이에요" for a statement and a question. Only difference between is your tone. When it's a statement, your tone at the end goes flat. If it's a question that ends with "~이에요?", you should go up with your tone at the end.