Do you have an Ontario Early Years Centre near you? In the city where I live this organization has a list of questions parents should ask potential HDCP's and if you look at the list it covers everything you should cover during an interview.
During the emailing or phone call stages I make sure parents have read my website entirely because it covers all my most important details - hours of business, fees and other important things. I ask them lots of questions at this stage to make sure I won't be wasting my time by having them come over for an interview.
I start my interviews with a tour of my daycare rooms, kitchen, dining room, toyroom, half bath for toilet training and tell parents how I have organized each room for daycare use during the day. Then I give a rundown of our daily routine and ask how they feel their child would fit in. I give out my resume and go over a few points in my contract. Then I ask them to tell me about themselves and I take notes, their jobs & locations, home location, child's behaviour and routines, and let the conversation move naturally along.
If we are in sync and conversations are moving along well I am willing to spend the time, but if someone comes in without their child or don't even take off their coat or have a clipboard and an attitude I try to move things along very quickly so I'm not wasting my time. Interviewing is a skill you learn as you practice, but you learn to spot the red flags and warning signals for families you don't want to have in your daycare.