質問 and 疑問: asking questions and having a doubt
Distinguish developing a doubt, asking a question, and resolving the uncertainty.
Asking another person
質問, read しつもん, is asking a question or the question itself. 説明の後で質問しました。 means asking after the explanation.
質問を紙に書きました。 means writing a question on paper. Whether it was actually delivered to the other person is separate.
A doubt held in mind
疑問, read ぎもん, is doubt about something unclear or unconvincing. その説明に疑問を持ちました。 means developing doubts about that explanation.
疑問が残っています。 says that a doubt remains. It does not report that a question has already been voiced.
Asking and resolving
疑問に思ったので、質問しました。 says that someone asked because they had a doubt. The mental state motivates the action.
質問しましたが、疑問は解けませんでした。 says that the person asked, but the doubt was not resolved. Asking alone does not establish full understanding.
Does 疑問が残っています mean that a question has already been asked?
Show the answer and why
No. It describes a remaining doubt. Whether anyone asked requires separate information.