Remove Date From Tooltip

You can filter the tooltip content using this filter: http://codex.wp-event-organiser.com/hook-eventorganiser_event_tooltip.html (please note that you will need to clear the cache by updating an event before changes will take effect).

For editing the title you can use this filter and change $event['title']: http://codex.wp-event-organiser.com/hook-eventorganiser_fullcalendar_event.html