(1) What are good influencing / convincing methods one can refer to while presenting such a story? For example, showing data, building trust etc.
From your question I think you may be missing one element in the flow of the story, which is the most critical.
The personal impact story needs to have a part where you show you had an “aha moment”, where you understood the real reason why the person was not agreeing with you. This is critical and without that, the story will be weak. The way you reach the “aha moment” depends on the story.
Once explained that you got to that point, the method you use to convince the person given the new knowledge may vary. The critical part is that you show you are aligning with the needs that you discovered. It could be showing data, having a new conversation with the person or any other way where you show you used the new knowledge to align with the real needs of the person. Whatever action you use, it should be specific and described in detail.
I developed a specific structure to be sure you deliver the stories in the best possible way (and no, is not STAR, PARADE or any other you may find around ;)), please feel free to PM me if you need help with that.
(2) Content wise, what are some of the ways a candidate can set themselves apart from the competition when answering a PEI question?
Most candidates use an incomplete structure that misses some critical elements. Both STAR and PARADE are not ideal (PARADE is not bad, but still not great). If you need help with that please feel free to PM me.
(3) How long should an ideal story be (1, 2, 3 or 5 min.) while answering a PEI question during a McKinsey interview?
It depends on how fast you speak, but around 5 min (for your part) is a good benchmark. The interviewer will usually ask questions on parts of the story, so the overall story will last 10-12 min.
Of course, just the fact you spend 5 min doesn’t guarantee the story is going to be good or well delivered.
Hope this helps,