Can you tag courses?
Yes, Managers and teachers can tag courses in Course administration > Edit settings > Tags for a course, and all users may search for them in Navigation >Site pages > Tags" and/or you can add the Tags block to your course.
Who can tag courses?
By default, the roles of Teacher and Manager can tag courses. Other users may be given the capability to do so in a specific course with a role override in Course administration > Users > Permissions where you can choose the role to add this ability to (e.g. Non-editing teacher), and then set the moodle/course:tag capability to Allow. See also Course tagger for how to create a specific system role to do this.
Can you display only tag courses in the Tags block?
Yes. When you add the Tags block to a course, you can specify that the tag cloud only show tags from that course, in Configure Tag block > Tagged items context and choose the current course from the pull down menu. (The course needs to have at least one tag already in it for it to appear on the list to choose.)
When someone adds an unsuitable or inappropriate tag, other users can click on the word (1) to get to the screen where they can flag it as inappropriate (2) The administrator can modify or delete inappropriate tags from Site administration>Appearance>Manage tags (3)