Hi Alex,
I am sorry for the delay of this reply.
Regarding the group counts in profile page, because the profile page is accessible by everyone thus we do not want to show 'invited' to other users. Other users shouldn't know of the existence of these groups.
Anyway, I've added a fix where if the currently logged user viewing their own profile page, the invited group will be displayed to user. Attached the modified php file, please download the file and copy the file to folder 'JOOMLA/media/com_easysocial/apps/user/groups/widgets/profile/' and overwrite the existing view.html.php file. Remember to backup the original file first before you apply the fix
The fix will be added into next release of EasySocial as well
Hope this help and have a nice day!