1) No, it isn't necessary but advisable for the sake of all parties.
2) Rover's training vids say to meet outside on neutral turf, which could be on the sidewalk outside your home. Clients come to my house because that way they can see where their dog will be staying. My dog does better meeting others inside the home (he's leash aggressive).
3) Talk about what you provide and what the client expects, any special needs the dog may have, his/her routine, pickup/dropoff times, food issues, medical needs,...anything. I give them my Dog Info Sheet, which they fill out and give back to me when they bring the dog over for his/her stay. It contains all the necessary contact info, vet info, as well as a section on behavioral characteristics (likes, dislikes, fears, etc.)
4) I think both parties would realize it, but at times owners have an overly optimistic view that whatever behaviorial issue will work itself out. You have to decide whether it is a good fit for you, your dog and especially your young kids. Be honest and upfront with potential clients if you have qualms and that you are sure there will be a better fit with another Rover sitter.
I think I've only bowed out of one potential engagement because the other dog wouldn't leave my dog alone (constant humping) and I didn't want to subject my dog to that 24/7. Don't overthink it. A meet and greet doesn't take very long and isn't stressful in the least.