To be able to binary search for an answer, you should know that:

If some value $$$x$$$ doesn't satisfy the requirements for an answer, then all values lower than $$$x$$$ (or greater than $$$x$$$, depending on the question) doesn't also satisfy the requirements.

AFAIK it's formally called a monotonic function. Definitely not a professional on CP but from what I've seen I can say that plenty of interactive questions or some "minimum number of operations that satisfy the requirements" involve binary search. As for Codeforces, the first three Div. 2 problems doesn't involve too many BS questions. Other than that, I can say that if there's an array that you can apply sliding window, you can combine these two techniques together, it's not uncommon.