I'm in the process of getting approved for being a "sitter" on Rover. The main reason I did this was just to make some money while walking MY dog, along with helping people out who need a sitter/walker. I also registered for Wag, but heard that Wag does not allow you to bring your own dog on the walks, so I wanted to see if Rover does.
Yes, on Rover (unlike Wag) that is a possibility. The client needs to understand and agree to this though. I'd suggest always set up a meet & greet in advance of booking the walks, to ensure it's a possible match.
I would discourage you from bringing your dog along while you perform walking services for a client
For me it all depends on your dog and its level of sociability and obedience. If you have a dog friendly dog who walks very nicely on leash, I have no issue with that. I find it can help dogs who do not walk so nicely on leash. But if your dog is very easily excited by other dogs or does not have enough obedience, it will only make things harder for you and your client's dogs might learn very bad habits. I found that clients with single dogs actually liked their dogs having a walking buddy.
Of course your clients would need to be made aware and I would never walk more two giant dogs, three medium to large or four small dogs at once for safety reasons and because I like giving each dog in my care a whole lot of attention.