You can ask the web host to install the plugin for you. The activity chooser appears either on a front page or in a course. The switch appears in the course administration section of the settings block in a course. (Your screenshots show admin pages, not course pages) See illustration.
It doesn't link when there are js conflicts.
Course administration appears in the settings block when in a course. The glitch is that the frontpage, where you may be experiencing the link problem, is just a pseudo course and hence doesn't have the course administration section.
For an alternate strategy try the Profile switches plugin which allows you to turn ajax and with it the activity chooser off. hth
Already implemented in the Dataform (should be released in the next version this weekend; see http://docs.moodle.org/23/en/Dataform_Notifications) . There is also infrastructure for per entry notfications/workflow management. So you can use the Dataform or suggest to HQ to employ a similar approach in the Database module for quick resolution.
There are qtype plugins that do that. See this post for one suggestion. You can also google moodle question type all or nothing to find links to other plugins.