Do I charge per walk per dog?

Rover allows you to set three rates for dog walking - your primary rate (the rate charged for one adult dog), an additional dog rate (the rate charged to the second or more adult dog(s) in the same booking), and a puppy rate (the rate charged for any/all dogs under 1 yr old, regardless of whether they are the first dog listed in the booking or not).

Personally, I charge the same rate for adults and puppies for walks. I don't find the amount of effort I have to put in for a walk differs depending on age - I'm spending the entire time with them actively engaged regardless. I also offer a discount for any additional dogs.

That's totally up to you; you are allowed to set your own rates. I personally charge a base rate for one dog, and an additional lower amount for the second.

You can hold in mind the size and activity level of the dogs, and charge accordingly. I gave a discount to one client who had two small dogs.