Is there a way for a walker to enable push notifications for "Available Walk Requests" on the Rover app?

The on demand program is not available in all markets and the help section hasn't been updated with info on the program. To answer your question I'm pretty certain push notifications aren't available but you can call Rover support and ask them @ [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]