I think a lot of people considering going for DM think of it as just another class. It really isn't like the classes you have likely taken to date. You will be evaluated on your personal skills, dive knowledge, and your ability to lead divers and prevent incidents from turning into emergencies. You will be seen as a role model for students and your skills should be at the level you consider yourself to be a role model. You should be able to instantly react to issues you encounter underwater and prevent a student from panicking if they are unable to resolve the problem on their own.
In addition to those skills you should have a broad base of dive knowledge. Things like dive theory, equipment (to include minor repair/maintenance), and physics are areas you should be familiar. Take a look at some of the questions asked on the basic and advanced scuba forums here on SB. Can you answer most of them correctly, not just making something up? These are questions new students might ask you and you should be able to give the right answer.
Unless you are traveling and doing one of those DM internships at a resort in return for room/board or similar compensation, expect your DM course to take 3-6 months to complete, depending on how busy the shop is that you are training at/working for and how much time you have to be available to assist with classes there. My course took a full four months to complete, and that involved taking several days off work and pretty much devoting all my free time to the program. Another guy in my class took over a year to finish his. If your situation requires long distance travel to get to a shop, this could be a real hindrance. The DM course is not something you can complete in a few days. You have a whole checklist of things you need to complete and it takes months to tackle all of them.
The internship portion of the course where you are actually working with students, watching over them, guiding them, assisting them with issues, being a go-between for them for questions they might not feel comfortable asking their instructor, etc. is where you really learn the role of the divemaster. The classroom and pool sessions you do with your instructor aren't going to provide you with a lot of earth shattering information that you don't already know, nor are they designed to do that. Your personal skills need to be at demonstration quality. If they aren't, the DM course is not designed to hone them. You might need to redo a skill or two for your instructor to be satisfied with it, but you shouldn't be all over the place in the water. TSandM's suggestion of comparing yourself to the 5thD-X videos is spot on. You can also check YouTube for UTD Essentials or GUE Fundamentals for videos of what you should look like in the water.
You asked about what questions to ask. I would find out from your instructor (and make sure you are talking to the person who will be YOUR instructor, not just someone who works at the shop--you want to know what your instructor requires) what the cost is [broken down into course costs, quarry/boat fees, required books/materials, any materials your instructor wants/suggests you to have in addition to the required items (they may want you to purchase some of the instructor materials--which some are useful to the DM course)], whether or not the shop will allow you to use your own gear or wants you to purchase their brands or if they will allow you to rent their brands when you are working with students, how often they expect you to be available to help/how often your instructor is available, what duties/tasks are you are expected to learn/complete as a member of the dive shop staff during your internship, where the pool/quarry/boat is, insurance costs you may have to pay and any dues to your organization you are responsible for, and their general expectations of you as a DM candidate.
I think a lot of people go for DM wanting to attain the rating just to have it, and a lot of that is due to the way Padi and other organizations push it as the "next step" in their ladder of training. If you aren't planning on working (really it's more like volunteering) as a DM, there really isn't a point in going through the course.
For me, I got a lot more out of my UTD Essentials course than I did out of my Padi DM course. If I wasn't actively assisting with a shop, I would see the DM course as a near complete waste of time and money. I really fail to see why people invest the time and money in the course and then never or rarely assist with classes after getting the card.
I don't mean to sound overly negative, but it is what it is. My wife went through the DM course with me and I think she had a totally different expectation of what the DM course was and would be. She got the card and helped with classes for about a year afterward, but is not an active DM anymore. She would have been completely happy remaining at Rescue level and then moving on to the Tec classes we have taken.
