I am not aware of this type of functionality existing in Canvas for discussion boards, but I could see why you would like for this as it could help other students who might have a similar question, but don't want to ask it or keep you from answering the same questions multiple times.
Currently the only way students can ask you questions without other students being able to answer (but other students wouldn't be able to see the question they asked), is for the students to send you a message using the #conversations functionality.
Hello @yara_locher ! @bneporadny had a great response. I thought that I would add that it appears as though this functionality has been suggested in the past, https://community.canvaslms.com/ideas/10548 (you may need to request access to view archived feature ideas). In the thread community members such as awilliams posted thoughts on work-arounds. Although this idea did not generate too may votes, as the feature idea document describes it is possible to resubmit an idea that has been archived, https://community.canvaslms.com/docs/DOC-14903
All the best---
Hello (again!) @yara_locher - In addition to Brian's suggestions, there a few other things to consider. There IS a Feature Idea that--while not exactly what you have in mind--could help you with this that you may want to consider voting upon: https://community.canvaslms.com/ideas/8974-allow-instructor-to-blockmoderate-student-from-discussion... . In addition, consider creating an unthreaded discussion (which is the default setting). The documentation calls these "focused discussions" on their lesson on creating discussions. I am not a fan of that particular description--and it is something easier seen than described--but basically it makes it less visually obvious how students can reply to one another, though of course it can be done.
That said, your concern is a valid one, since I often recommend to online faculty, especially, that creating an "FAQ"-type of discussion is a virtual must in any online course, as it serves this exact purpose of having students ask questions relating to the class in general. One suggestion is if you take @bneporadny advice and have the students communicate to you directly--especially for an online class--would be to gather the questions and then post an Announcement answering them for all of the class to see. Furthermore, as that documentation shows, by default Announcements can NOT be replied to. So they can send you the question privately, but if it is not student-specific and more about the class in general you can post the answer on the Announcement page.
(To somewhat allay your concerns, I can state that some instructors would absolutely love for students to contribute more to any discussion, so you may not have anything to worry about just going with your original idea of creating a discussion! )
For an FAQ Discussion Forum that provides answers but does not allow students to comment, is it not possible to use a 'closed for comments' discussion forum? This way the instructor can add questions and answers that the students can see but can't reply to. Would this work?
@yara_locher Welcome to the Canvas Community! You've gotten some great suggestions so far. For what it's worth, when I was teaching, I would ask students to feel free to message me directly with their questions, and when a student sent me a direct message asking about something in the course, I would (of course) reply, and then add the question and answer to a page called "What Your Fellow Students are Asking" or "Frequently Asked Questions (FAQ)." I would place that page in a Course Resources module at the top of the modules list so that students could refer to it regularly.