The verb “有” can be used together with both. (有疑问 有问题 both correct)
The verb "问" can only be used together with 问题（问问题）（问疑问 sounds weird）
问题 is just like a question. When you have a 问题 for me, maybe you don't know the answer, so you wish to find the answer by asking me the question. But it's also possible that you do know the answer and just want to test me.
疑问 sometimes can be a question, but it must be a question with doubt. When I have a 疑问, that means I just don't know the answer.
老师问了我一个问题。（The teacher asked me a question.）
It's not proper here to use 疑問，because the teacher is supposed to know the answer.
(I have a question: Why don't you want to get married?)
In this sentence, 问题 and 疑问 are both correct.
“疑問” is just to emphasize the doubt.
hope it helps ^^