In my internship book, All Work, No Pay, I talk all about internship interviews -- I even provide a list of the most frequently asked questions during an interview. Everyone always tells you to ask questions at the end of the interview. I always encourage students to ask questions that relate to the internship as you are taking this time to see if the internship is the right fit for you (just as the employer is evaluating whether you're a fit for their company). For example, I run a virtual internship program (you intern from home). A great question for students to ask me during the internship interview is, "Could you go over the daily tasks that I would do as an intern at your company?" OR "Since this is a virtual internship and there won't be face-to-face meetings, how do we communicate?" OR "In your opinion, what makes a great intern for your company?"
2. Asking About the "ME" benefits. Every internship is going to benefit you. Not only are you going to get a hands-on learning experience and learn about an industry of interest, you will also meet great people and start to build your professional network. Asking how the internship will benefit you or how many professional contacts you will meet is not appropriate during the interview. You don't want the employer to think you're disingenuous or are going to "steal" their contacts. You will organically gain the respect of professionals in the office by doing a standout job at your internship.
3. Reporter Questions. I had students asking me about my feelings on paid vs. unpaid internships, internship lawsuits and sexual harassment benefits for interns during the internship interviews. I speak to reporters all day about these subjects and I'm happy to share my thoughts in the proper setting. When a student is trying to get an internship and only has 15 minutes to prove to me they are the best intern for my company, these reporter questions are frustrating and off-topic. Once they land the internship, I'm happy to set aside time to have a discussion. Even if they don't get the internship, I'm happy to have a discussion. You have to "know your room" -- what kind of discussion are you having and is this the appropriate time to ask that question?