Thread:Project:Support desk/Special page access, Purge access, and template storing (2)/reply

Purging is possible for everyone and can't be restricted. You could set the user right  to false for every user group you want, but that would only require the members to click "ok" for the purge action.

For preventing access to certain (special) pages, you should read Manual:Preventing_access, MediaWiki isn't designed for that.