searching Time Machine backup data

so I get how to browse of Time Machine data; you can see what your backup's state was at any time.

How do you:

• see what files have changed between two successive backups
• find which backup has the last copy of a particular file, before that file was deleted?

For your first question: see the references to TimeTracker (GUI) and timedog (command line) in What is Time Machine doing? on Server Fault.

To find a specific file see Mac 101: Time Machine:

You can also perform a Spotlight search in the Finder to find a file. Simply type the Spotlight search field and use the back arrow to have Time Machine search through your backups to find what you are looking for.