I've a Skype interview for PhD application (it will make me miss one of my classes today.) I've been asked, in advance, to prepare a short presentation and then there would be some discussion with the panel (I guess.) I expect that they will ask if I have some questions so, I'm wondering what are the best (type of) questions one might consider?
It is not mandatory to ask questions. Generally they offer you the opportunity to ask questions in case you are not sure or confused about anything or any process related to application/lab/university.
When I had given PhD application interview almost all times interviewer asked me if I have any question. I didn't ask questions for most of the time. However few times I do asked question specially when position they were offering had partial financial support from supervisor. That case I asked about chances of getting rest of financial support. They were quite helpful and actually suggested me to check for RA positions in other related departments. In another case, I asked professor about possibility of collaborative work because I was interested in some interdisciplinary work. He was very impressed by question as it showed that I had already focused area of interest.
I also remember few of my friends have asked questions like, "Are there many flowering plants around campus because I am allergic to pollen-grains?" , "Can I get accommodation on campus if a dependent is accompanying me? ", "You were working on XX problem before are you still working on that?" etc.
You should ask questions depending on university you are applying and professors interviewing you. Do some basic research on their background from university web page. Don't ask cliche questions and don't ask for the sake of asking.
I guess, your presentation topic must be in alignment with the interviewing professor's research area so IMHO it's best if you ask some questions like (1) What is the future plan or goal of that research i.e. some abstract model or a prototype etc. (2) You can discuss about your ideas which you got after reading any of his paper.
One of my favorite go-to questions is along the lines of "why should I choose you?" Basically, ask them what makes their research group different or special, compared to other places you might be applying for. You could research X at a million different places, so why is institute Y the best? I think this question is great for a few reasons. It's nice and open-ended, and you'll often get an interesting response that can give you some insight into the group. It's a versatile question, so you can ask it literally anywhere you interview, but it still has more substance than "when's lunch?" Finally, it puts an ever-so-small amount of pressure on the interviewer by shifting the dynamic so that they're trying to impress you, rather than the other way around.
Of course be a little gentle with the phrasing of the question. Something like, "I've been applying to a number of PhD programs, and I know that Institute Y is one of the best departments with great faculty and an excellent lab. I've been wondering, though, what do you think makes this place unique, or what's different about it compared to some of the other top-tier research institutes?"
you should ask something around the lines: What qualities do you think I am missing, that would make me a better candidate?
He will tell you what he perceives as your weak points and give you a chance to elaborate.
Student: What qualities do you think I am missing, that would make me a better candidate?
Prof: It would be nice if you have more publications
Student: I didn't manage to publish anything yet, however we have 3 manuscripts submitted, 2 in preparation and I am a columnist for 'Cats and Dogs' magazine.
Prof: You're hired!