How involved is this person (or group) in the day-to-day function of the job?
Whether the person is fairly removed from the day-to-day function of the job you are interviewing for or very present in your possible day-to-day functions will make a difference in his or her interviewing you.
How has he or she felt about other candidates that you have sent?
You'll find out if you are the first or one of many.
Does he or she usually agree with your opinions?
Rarely are you ever going to hear a hiring authority claim that his or her superiors never agree with him or her. Don't ever believe a hiring authority if he tells you that his superiors always agree with them. It is more reasonable to hear the hiring authority say something like, "Most of the time, they do."
You might want to get into a conversation about what the hiring authority and his superiors may or may not agree about. This will give you insights into the relationship between the hiring authority and his or her superiors.
What is this person going to like or dislike about my experience or background?
Try to make the hiring authority tell you where your strengths or weaknesses might be in the eyes of the next interviewing authority. You will be surprised what you might learn.
What have you told him or her about me?
Sometimes a hiring authority will only send one or two people to a superior. Sometimes she will tell the superior who she thinks will do the best job, sometimes she doesn't. You need to know what she has told the superior so you know how you stand.
How many people is this person going to interview?
Are you one of three or ten? It makes a big difference. It doesn't hurt to ask what succession you are in the interview lineup. If you are the first of three, there is a tendency for you to be the one to "set the bar." If you are the third of ten, you may not be remembered. You are going to have to do a lot of active follow-up to be remembered.
When will this person get back to you with feedback?
Most people assume that the person or persons who do the second interviews will get "right back" to the hiring authority. Wrong! Don't be surprised if you hear, "Well, she is going on vacation next week for a week and will get back to me when she gets back." Not good news. You will have a tendency to think the feedback will be immediate.
How do you stack/rank the candidates? Am I your strongest one? Are you going to recommend me as the best candidate to your superior?
This is a great question and really tests how you are doing. Most hiring authorities will be taken aback a bit at your boldness. But this is a great test of where you stand. And, after all, you need to know. Listen carefully to what the hiring authority says. If he or she says that you are one of many that is talking to the superior and that he or she does not really have a favorite, then you need to be on your guard. It is likely that you are simply one of a number of people that the hiring authority is sending up a ladder. It is not likely that you are considered by him or her to be the strongest candidate.
If the hiring authority says something like, "Well, I have two candidates that I think can do the job, and you are one of them," then you know where you stand.
Sometimes, hiring authorities will simply try to find two or three candidates that can do the job, send them to their superior get this superior's blessing, then choose one. Most of the time, however, the hiring authority has one or two favorites in the group. If he has a long-standing relationship with the superior, he will probably tell his superior whom he likes best. But you will never know this. So, it is best not to take any chances. Ask the hard question of, "Where do I stand with you and are you going to tell your superior that I'm the best candidate?"
Unless the hiring authority says that you are his strongest candidate, then you need to ask a question along the lines of, "What do I need to do to become the strongest candidate?" and then shut up. A confident hiring authority will be very impressed with your courage to ask these difficult but telling questions.
How This Affects You
Remember that your purpose and goal of an initial interview is to get to the second and subsequent interviews. You want to be sure that the questions you ask "position" you at the top of the list. Every question you ask should not only give you information you can use later to decide if you will take the job, but also demonstrate your intelligence. If you ask intelligent questions, you will know how to sell yourself "up" the interviewing ladder.