I would like to create a calendar and display it on a page. How do I do this?
This is possible in Confluence. Follow these links for the Atlassian documentation:
Create Calendar: Create, Add, and Edit Calendars | Team Calendars Data Center and Server 6.0 | Atlassian Documentation
Display calendar on specific pages: Embed Calendars on Confluence Pages | Team Calendars Data Center and Server 6.0 | Atlassian Documentation
The following links could also be of interest:
https://info.seibert-media.net/display/Atlassian/Confluence+Team+Calendars+Plugin+-+prices+and+costs
https://confluence.atlassian.com/teamcal/subscribe-to-and-from-team-calendars-273285883.html