Translation:That is a very difficult question.
There is a bit of overlap in their use, especially with things like homework/testing, but they're similar to "question" vs "problem" in English.
質問・しつもん is a question or inquiry, something you ask that simply needs an answer
問題・もんだい is a problem or issue, something that needs to be solved/responded to
What’s the difference between “That question is very difficult” (incorrect) and “That is a very difficult question” (correct)?
The difference is that in the correct answer the subject is just "that" as opposed to "that question"
そのしつもんはとてもむずかしです それはとてもむずかししつもんです Theres not really any difference i can see in the question itself, but its important to see be able to see the difference at least
No because only what comes before は is the topic and in this question 'that' by itself is the topic.