Is there a place to leave notes about the dog/s who stayed with me, without the owners seeing it?

The Notes section is not seen by owners. It is for you alone. There are instructions on how to write notes here:

https://support.rover.com/hc/en-us/arti…

In your inbox, on the "past stays" tab... there's a button that says "leave review". The next screen asks you if you would book the dog again and has a place to write internal notes for future reference!