Could you tell me please which line i need to remove to dont show the online status into the GJ Events?

You'll need to modify the showEvents function of the event plugin below to alter its display.

components/com_comprofiler/plugin/user/plug_cbgroupjive/plugins/cbgroupjiveevents/cbgroupjiveevents.php

also i need to remove category name into "My invite"

See the below template file for My Invites display and modify as needed.

components/com_comprofiler/plugin/user/plug_cbgroupjive/templates/default/tab_invites.php

Basically any of your design questions can be covered by checking the relevant template file of the location you're at except for integrations as integrations display is done in the plugin it self.