Thank you for your question.
Do you mean appointments or resources? They are very different entities in a GroupWise system.
An appointment is a message type. They can be posted (i.e. personal), or group appointments, sent by one person to many recipients. In order to access any message type own by another user (including appointments), you need to have been granted proxy access to the owners account, or use a Trusted Application object to access the account (requires Administrator rights).
A resource is a system entity like a user object. While I have not shared your specific need, I suspect you would use the Object API to conduct a busy search on a resource in order to check it’s free status. See http://developer.novell.com/ndk/doc/gwobjapi/gwobjenu/data/hgqg2qlg.html as a starting point.
I hope this helps.