I am not sure what I have missed. I first installed BAT module,but later decided to instead use Rooms module. I am under the impression that Rooms will make use BAT FullCalendar , I could be wrong. Unless if there are some configurations needed. Or must I uninstall BAT completely and only use Rooms module with a normal fullcaleder module? I have checked permissions but could not see anything funny. See attached. Thanking you in advance.
Rooms and BAT are separate modules, you should fully un-install BAT and then follow the Rooms installation instructions. Rooms depends on the fullcalendar library, but not the full calendar module.
Within the Rooms module there is a rooms.make file which will download the library if using Drush or you can visit https://github.com/arshaw/fullcalendar/releases/download/v2.6.1/fullcalendar-2.6.1.zip to download it. The FullCalendar library should be placed in sites/all/libraries so that you end up with the file located here: sites/all/libraries/fullcalendar/fullcalendar.js
(quoted from http://docs.roomify.us/rooms/installation.html)