Unfortunately that Easysocial user module do not have an option to exclude user, but you can disable this setting exclude site admin in user listing page https://monosnap.com/file/WIZjYovKStUSONQML5kmViFEXdTiRQ .

If you only want to exclude it from the module, you have to modify on this file JoomlaFolder/modules/mod_easysocial_users/mod_easysocial_users.php

LINE 76

$options['includeAdmin'] = $admin ? true : false;

Replace with

$options['includeAdmin'] = false;

Regarding that online indicator, you can download my attached file then replace into your current template override file location :

JoomlaFolder/templates/yourCurrentTemplate/html/com_easysocial/helpers/avatar/user.php