Goinggetstough my understanding is that about one third of applicants sit the Westminster Challenge, not all of whom expect to get it, and indeed several who do get it turn it down because of the boarding requirements and become Honorary Scholars. My understanding is that Westminster like boys to be prepared for their own exam, in part because the maths paper takes a more analytical approach.
The Challenge is marked in May a month before CE. If you dont do sufficiently well in the Challenge you can be asked to sit CE. I suspect that this would be a trigger for prep schools and parents to start looking for back up options.
I dont think many fail CE, though DD has a friend who did. We do know boys who were told by their Preps that they needed to raise their game and focus more if they were to hit the mark.
Boys change a lot between 11 and 13 and we know of several who change their minds, especially about boarding. Most will decide by the time big deposits are due, but some sit on offers for much longer losing both a deposit and a first terms fees.
Westminster and St Pauls often seem to hold exams and tests on the same day. I assume the idea is that a boy who is good enough for one will be good enough for the other, and it helps the school by forcing parents to decide in favour of one or the other. They are very different schools.
My understanding is that the pretest happens in batches, so is not a one off pass/fail event with a certain number getting through. Schools have to actively manage their waitlists and relative popularity waxes and wanes. Coming top of the FT table several years in a row has sent world wide demand for Westminster's sixth form pretty much off the scale. Because the boarding is weekly not full the school is less accessible for international students at 13+, but I assume interest is rising.