I can answer one of your questions, which is no, schools don’t recruit for JV or thirds, and most don’t recruit for most varsity positions! There are definitely exceptions to this: if a school is a national powerhouse in the sport, then yes, there is more recruiting. But at selective boarding schools there actually isn’t that much recruiting going on.
For example, the sport I know best, soccer, South Kent recruits super heavily, and is right up there as possibly the best team in the country. Hotchkiss maybe has one player on their radar that they hope to land but the coach has little pull. And I believe that’s true of other sports at Hotchkiss.
So it really depends on the school and the sport.