You can ask whatever you like, but try to ask questions during down time or while the doc is charting, washing his hands, looking at an Xray, etc after leaving the patient room. Some guys aren't real keen on you firing off a lot of questions in front of the patient, esp when you don't have any training and don't even know the anatomy, path, etc yet. If you are in a surgery situation, ask beforehand where to stand and stay there; for surgery or procedures, it's also probably best to limit questions until afterwards since you don't know which parts of the procedure are technical and require his focus.
Some good open ended questions are best to let the pod answer at length and will prompt you for more question ideas:
"What were the most challenging parts of podiatry school, and what are some strategies for success?"
"I see on the wall plaque that you trained at X school?"
"How has your practice changed over the years?"
"What kinds of hobbies do you enjoy?"
Also, it's likely that you'll be left in the clinic room alone with the patient, at least briefly, a few times as he runs to the office, phone, etc. Don't touch or help the patients unless you are sure it's ok with the pod (that even goes for seemingly harmless stuff like helping them into the chair, taking shoes off, etc); you're not covered under the office or hospital's malpractice and you some guys are real strict about that stuff. If the patient asks you personal stuff about school, interest, sports, etc, it's fine to be polite, but be sure to re-direct any medical questions to the pod with a "I'm here to learn too... why don't we ask Dr. X when he gets back?"
You will get a feel for the DPM's personality after a few days, but try to let him initiate most of the conversation early on, especially in front of patients. Most importantly, just be on time and be interested. A "thank you" card and a box of chocolates for him and his office staff on your last day is also a nice gesture; they're not getting paid to teach and are just doing it to help you gain insight.