What does it mean when it says a sitter "has no dogs" and their profile no longer exists?

Yes it sounds like the sitters have deactivated their profiles. So you will either have to search again or call Rover Support @[Edit: Rover’s contact options have changed. Visit the Rover Help Center at https://support.rover.com/ to find the phone number, help articles, or chat with the team] and they will work with you to find a great sitter in your area, there is no cost for this service.