You should see options in user roles that will either allow, or disallow capabilities by user role. If you create an admin user role, and assign your admins to that role, you could give them the capability of asking a question, and leaving other roles with the capability of responding.  You can add the widget to the right sidebar, if the theme has one, by customizing the index page, and dragging the widget to the sidebar.

Please check this plugin, Lev: http://www.oxwall.org/store/item/156

Unforunately, default software functionality does not have such an option.