I want to apply for a Ph.D. position in a group where there is only their research summary written on the homepage. An applicant should write a research proposal and if the PI likes it then they will offer a position. I have gone through their publications and tried to figure out what can be done more. This is a very big research group so the number of publications is huge too and they work on so many topics. Every time I came up with an idea I found that it’s already done or other groups are working on that. Now I am wondering if I write the same thing, they might think I copied the idea when it is not the case. Also, some of the techniques I have done earlier and some never. Now while writing the proposal can I write some methods I never did? Can they ask questions like if you have never did it before how can you do it during Ph.D.?