Ds had summer reading and I think maybe a writing assignment associated with it before grade 9. Nothing else that I recall. But there was always a bit of summer work.
Totally agree that it’s best to just take the placement tests without preparation. Our school, and I am sure most others, made sure it was easy to move up or down if the level was wrong without any other scheduling upheaval.
Roughly, they will require 4 years of the 5 main subjects (4+FL, and as @skieurope said the FL needs to be through level 4 in one language). A few ask for a year of art or music, although that isn’t that common. I have seen that Wesleyan has said that it isn’t required that kids have calc, but most do. I would assume that means that most schools on that level expect it unless there is a reason it wasn’t taken.
The good news is that at my LPS, I have to be on top of all of this, because no one else is, including the GCs, who I have educated on several aspects of selective school applications over the last few years. I would be shocked if a kid gets through BS and then finds out he isn’t meeting the requirements for selective colleges. The BSs know they are judged in part by the colleges they get kids into, fairly or unfairly. So they will be doing everything they can to make sure your kids gets to a good place that is at the right level for him/her.