First, regarding the backup operators group:
it is a local or global group that contains the user rights you need to back up and restore files and folders. Members of the Backup Operators group can backup and restore files and folders regardless of ownership, permissions or auditing settings. In short, it allow you to bypass permissions for your files.
You can find more info via Google.

As for the "Track local deletes" option, it does what it says in the tool tip:

The software places a special marker in place of a file when it gets deleted, so the next time you restore files on a different PC the application will be aware of that and you're be able to use "Restore deleted files" option. This is basically the only case where this option is needed.

Now, regarding the last question:
Nothing special will happen. Both options will work in conjunction with each other. The files in the cloud will be purged after they get deleted locally, and thanks to "track local deletes" option a special marker will be placed in the cloud to identify deleted files when restoring the data on another machine.

First, regarding the backup operators group:
it is a local or global group that contains the user rights you need to back up and restore files and folders. Members of the Backup Operators group can backup and restore files and folders regardless of ownership, permissions or auditing settings. In short, it allow you to bypass permissions for your files.
You can find more info via Google. — Matt

Assuming, administrator of a PC or a Server or a domain controller has that rights never used that before.

Matt please explain why in some cases we need to restore data on another machine. Assume that is the same machine, a file is backed up and then deleted locally. If both options are enabled what would happen?

Sorry, I was not clear enough in my latest message. In this case file gets deleted from both sides and that's it. "Track local deletes" only serves its purpose in one case: if you're restoring your data on another machine and select "restore deleted files" option. The software checks which files were deleted from source and restores them.