PreciseKill welcome to Flarum!
Permission to make tags: currently the tag management is part of the admin panel and there is no way to give selective access to the admin panel (you need the admin role, and admins can edit anything). There are no plans to change this behavior at this time but suggestions are welcome!
Clarify moderation actions: could you elaborate ? We are currently working on splitting "edit user" into multiple permissions for the next beta flarum/core1965
User search feature: this is currently part of the "View user list" permission. How would you suggest to separate this permission? Currently this permission is needed for everyone if you want mentions to work.
Stickies continue to show at the top even after reading them: I don't see how this relates to a permission? An extension can be made to implement that behavior. I was almost certain someone had made it already, but I can't find any at this time. Stickies already stick to the top when viewing an individual tag. The choice was made to move them down on the frontpage so that users can see the new content without being bothered by pinned discussions all the time.
Manage groups permission: can you elaborate ? The whole permissions feature is group-based.