My client is doing drop-in bookings on a repeating weekly basis, but it will change constantly. She says she cannot modify things on her end, but has to call rover support. Can she? Or should she just create new bookings every week instead?

Weekly bookings may be the easiest to manage for both you and the client. However if you are lucky to have the recurring booking option enabled you the sitter can manage the weekly changes with a couple of clicks in the App, the client is charged weekly and your are paid each Tuesday.