How do I handle a client requesting house sitting for 1 animal whereas it's actually 7-9?

Wow, that's a lot of animals! There are take two steps you can take to ensure the pets' safety and well-being as well as a fair price for the care you'd be providing:

1) Tell the potential client that all animals in the home must be registered on their Rover profile in order to be covered by insurance during a house-sitting booking. I've had clients who didn't register a non-dog pet because they couldn't figure out how to do it. (You have to add the animal, then select cat/bird/etc. from the 'breed' dropdown menu.)

2) Give the client your rate per additional animal. Set a price in your profile by going to Services/Rates-->Rates-->More Rate Options-->Additional Dog Rate.

If they balk at either or both of these requests, I'd recommend declining the booking. There are just too many things that could go wrong.

The client must list each animal on their profile, like Micah said, in order for it (and you) to be covered by insurance. There is a category for cats, and I guess they could just select cat for the bird and the fish. Is there an 'Other' category?

Definitely charge them for all the animals, not just one dog. That many animals is going to be a lot of work, and you should be compensated accordingly.