>> Is this possible at all?
Yes
>> Im new to Exchange development but do have Design and Implementation experience.
So the best place to start would be
https://msdn.microsoft.com/en-us/library/office/dn567668(v=exchg.150).aspx and start writing some code that access mailboxes and calendars.
>> Get all rooms
Use a Room List
https://code.msdn.microsoft.com/office/Exchange-2013-Get-a-room-0eada812
>> Find all appointments which are reoccurring
https://msdn.microsoft.com/en-us/library/office/dn495614(v=exchg.150).aspx
>> Find all appointments where the organizer no longer exists in AD/Exchange
You will need to develop something to do this using the properties from the Meeting object (eg the Organizer property will give you the Email Address (or possibly only the X500 address if the user has been deleted)
>> Cancel these meetings.
The Organizer is the only person that can cancel a meeting, you can delete the Meeting object from the Room mailbox but this won't affect the copy of the Meeting held in the Attendees mailbox. What you should do is before deleting the Ex-Employees
Mailbox is find any meetings that need to be cancel and then Impersonate the User
https://msdn.microsoft.com/en-us/library/office/dd633680(v=exchg.80).aspx and submit the cancel the meeting using
https://msdn.microsoft.com/en-us/library/office/dd633667(v=exchg.80).aspx
Cheers
Glen