Apologies for the delay in getting back to you on this. I’ll try and touch on your questions without getting too long-winded. The overarching answer to all of your questions at once is that there isn’t a singular/ideal/perfect rep scheme that if completed correctly will magically result in the performance you’re looking for. In reality, the answer is much more nuanced based on your current output and timeline. Books like TftNA and even Special Strength Training prescribe templated rep/set schemes as a way of putting a pin on a map, but they shouldn’t necessarily be taken as gospel. That being said, let’s go after those three questions you asked in your post:
1) As an extension to the above, the short answer is no. However, various methods exist for adding variety to your current workload. For example, pyramids, density sets, basic circuits, etc. are all options that may help you bust through a plateau if you haven’t spent much time with them before. I can dive deeper into some of those if you’re interested.
2) Generally speaking, for improving muscular endurance you want to think about progressing volume (sets, reps, time, duration, etc.). Virtually every selection event is a test of work capacity, and while being able to use a heavier weight with a push up is nice, it’s not necessarily going to create the physiological adaptations that we’re after for the test. I’ll usually prescribe submaximal sets and build volume over time, and then when it becomes too excessive for a single session, I’ll play with frequency by sprinkling additional doses through the training phase.
3) This is essentially a question about what’s called “functional training volume.” With tactical events, this becomes challenging because as you mentioned, we often don’t know the duration of a test in advance. That being said, there are some assumptions we can comfortably make based on anecdotal evidence, previous exposures, etc. In my experience, an unbroken set of 80-100 push ups is adequate for a testing environment. Likewise, 20-25 pull-ups and 100+ sit-ups will usually do the trick. Once you find that you’re able to achieve these volumes comfortably, I’d have you introduce fatigue into the equation by hitting an assault bike, ski erg, etc before a set of bodyweight exercises to sort of simulate what you might feel during selection.
I know I probably didn’t dive as deep as you’d like into some of those questions, so if you have follow up thoughts let me know.