Marco, presently our Group plugin is just a light version of any group system. There are a lot of things still should be done for its functionality and this is what we are thinking about within the small team.
In the meantime the Group plugin has an invitation page where users can see the list of received invitations.  To see this page go to the Group page and click the Invitations tab.
So, if you need an additional feature the List of sent invitations, this is considered as a custom code modification.

Concerning the mail notifications you can manage this setting for group invitations via "My Preferences"> Mail Notifications page.

If you are not familiar with the code modification or plugin development, it would be better for you to find a developer who can help you. You can do it here: http://www.oxwall.org/market/specialists

Or if you sure that some kind of new feature for group plugin is really essential for all oxwall users, feel free to submit your improvement at Oxwall uservoice: http://oxwall.uservoice.com/forums/13756-ideas-for-oxwall .