In addition to answers provided:
Ask them to show you their preferred walking route in their neighborhood if there is one.
Ask for their vet name, address, phone and after hours vet information and confirm who to contact if emergency
Also request they authorize and give consent for you to contact vet re. care if they can't be reached (some contact their vet and tell them the name of sitter before the stay; for those that don't I ask them to date, sign, and write a simple statement of authorization to treat on a sheet of paper that is readily accessible, like in the kitchen.)
How do they prefer to be contacted (phone, text, email, etc.)?
Regular routines at home (especially if exercise or anti-anxiety measures)
House rules, such as where dog and you are/are not allowed, expectations regarding kitchen, phone/internet/TV, etc. privleges
any food aggression, very important if there is any history of aggression towards other in house pet, commands to keep the training, how many treats per day, behavior with unknowns dogs during walks
I always ask if they have special instructions for me. This is a non-confrontational question that allows pet parents to mention things like "Fuzzy does not like to get too close to strange dogs on his walk". If they have no instructions, I just ask what "Fuzzy" enjoys doing (walking, playing ball, treats, etc.). I hope this helps.
What does the dog enjoy the most? Walks, runs, cuddle time. Allergies? Feeding schedule?