"Doubt" is countable. It can be used in the singular or plural, depending on whether you distrust one or more things.

Keep in mind however that “doubt” signals distrust or disbelief. It is used when you don’t have confidence in someone or something, or reason to believe that something is going to go wrong in a situation. If you tell your teacher you have a “doubt,” your teacher may think that you do not trust her.

Example: I have doubts about marrying Gregory because I don’t think he really loves me.

“Question” is when you want additional information.

Example: I have a question about the perfect tense.

You may have both doubts and questions, or doubts and then you ask questions to clear them up. If you want more information you have a question. Most likely in a classroom situation you will be asking a question, not a doubt!

Source: https://www.gonaturalenglish.com/question-english-vocabulary-lesson/