I can't answer all your questions, but here's how I use the BM for my AD geldings:
Place all geldings in her care as Day1/Day2/Day3 (example: Monday/Tuesday/Wednesday) for Dressage/Cross Country/Show Jumping
If the BM deems them as competitive for any of those disciplines, they end up being entered.
So for example, if one of my geldings is currently only competitive in CC, he will only be entered in that discipline, which means he'd only be in 1 show that week. Obviously not ideal - so after the BM is done with her 3 days of showing, I go through and manually hand-enter my horses who are in the green. I could technically skip doing this, but it's easy to mindlessly go through entering greens & it maximizes my profits, so win win.
Once a gelding hits level 10 in a discipline, their training is switched to one of their other non-10 disciplines. The BM is much more efficient with SD geldings, so these guys won't need any hand-entering. :)
I hope this makes sense! Feel free to message me for any needed clarification.