Is it on-topic to ask for problems concerning a certain subject matter? For example, could I ask for something like "counting problems involving the Euler totient function," or "problems involving the Vandermonde determinant"?
Historically this is not how the site has been used, but it is an interesting idea that would be useful to a lot of people.
A major challenge in self-learning of mathematics is finding good problems to work on. Even when taking classes, sometimes the problems assigned are not what the student needs to understand the material. Some problems are more effective than others at promoting learning, and it is hard to know which ones are the best a priori. One can always pick up several books and work all the problems, but this takes so much time that realistically it is rarely done. This is especially true of self-learners who are not full-time students and have limited time to study.
Also, there are many places throughout the world where getting access to high quality books with problems is not so easy. While there is a great deal of material online now that explains mathematical concepts (e.g., wikipedia articles, recorded videos of lectures on youtube, course notes pdfs on university webpages, etc), there is a surprising lack of coherent well-thought-out problems sets online for many subjects.
There would definitely be value in having an online website where people can pose problems that can be upvoted and downvoted based on their usefulness to someone at a given stage of learning. Whether or not math.stackexchange is the right site is not clear. For this reason I think such questions should be tentatively allowed.
In principle, yes, however a specific instance could easily be "too broad."
If you ask such a question, make sure to be as specific and detailed as possible to explain what you are looking for precisely. In particular, it can be helpful to explain why you are asking something.