Given that you're going to be interviewing/shadowing in a medical office, I think approaching it as any other type of office (with a bit of the medical stuff thrown in) would be a great way to go. I would probably ask things like the following:
How many patients do the physicians see on a daily basis?
Do you typically work for one physician, is there a rotation, or does it change day to day?
What's your favorite part of your job?
What's the most challenging thing you deal with?
What qualities make the best fit for this position?
If they have a website, make sure to look at that and see if there are new things going on, such as a new procedure being offered that you could ask about.
I have worked in medical offices for 10+ years and I know these types of questions would give me the impression that the candidate cares about the right fit, for both the office and the candidate. Good luck!