Field Level Security for non-Admin users in Professional Edition Org is granted by making sure that all the fields are present on the respective Page Layouts for CalendarAnything custom objects.

As an Admin, and for each of the Custom CA_ objects
1. Go to Setup> Create> Objects
2. Select the object and go to the Page Layouts section
3. Edit the Page Layout to include all fields on the Page Layout

CalendarAnything Custom Objects:

CA_Calendar
CA_CalendarByUser
CA_CalendarToken
CA_CreatingField
CA_Filters
CA_Groups
CA_GroupsMembers
CA_HoverFields
CA_Sites
CA_UserSettings
CA_WebCalendar