I have been asked the first one before. Though they phrased it more like specific things I wanted to learn about in grad school (i.e. statistical analyses and research methodologies). I've also been asked:
how I would manage my time as a grad student between classes, research, teaching responsibilities, and etc.
what my dream research project would be if there were no restrictions/constraints regarding resources (I've been asked this a few times)
and vice versa, a research project I could pursue that would be feasible for a first year graduate student (i.e. with limited resou