"Please answer the three questions."
こたえる is always preceded by a に。In the Japanese language, the act of answering is thought of as "answering to" something instead of just "answering something," which might explain why "に" is used instead of "を"
The を particle is used with some intransitive verbs, for example「建物を出る」(leave a building) or「犬を怖がる」(afraid of snakes). It's not only the direct object.
I think an example that might make the particles clear might be something like 「私は第三の質問に月曜日をかえりました。」 I answered "Monday" to question number 3. I might be wrong, so if anyone more experiencedwith Japanese wants to come in, it would be appreciated.
Why is しつもん wrong in this instance? There are no context clues and it means question (whereas もんだい means problem in general)
I thought 問 was the counter for questions, but they're using つ here, is that normal?