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.?
First of all, the research suggestion does not reach to be able to contribute to the professional environment. In fact, this condition is not required for your degree in now. And, this isn't searched. However, while will give any suggestion to the environment; you have to especially interpret the same topics by a high-level English and the using technical tools which no one minded upon them in more before.