I developed and mantain the Frontend User Manager extension that can show exactly that listing in the frontpage.
The current 0.0.6 stable release does exactly that and if you need user management in the front you can give a try to the 0.1.0alpha13 release.
I think you are aware, that you can create hooks on install process.
Here is my approach, where I after install publish plugin as an example
This information does exist in the frontend model, but for whatever reason, isn't actually displayed.
Copy /components/com_users/views/profile/tmpl/default_core.php to you template directory, so /templates/yourtemplate/html/com_users/profile/default_core.php and then in said template, you can dump the data object which will show all of the above, and more.
Toolbar isn't really supported in frontend. In backend it's rendered by mod_toolbar module which is only available in backend.
You can still render the toolbar in frontend using this code but it may not necessarily work correctly:
Thanks to @Lodder for providing the code below which is very helpful
defined('_JEXEC') or die('Restricted access');
public function __construct()
$this->baseurl = 'https://www.eventbriteapi.com/v3/users/me/events?token=mytoken';