No, Widd.
You can enter a
max of 4 horses per event. However you can enter one horse if that suits you better. And it's per event type, not section. So for example, you can run 4 Reiners, and 4 Trail horses, or 2 Reiners and a Trail, etc and so forth.
As for events, once entries have closed, Bama will work out the event schedule. You will be required to enter all the events that you are placed in. Not to enter them is effectively pulling out of the competition. You'll have until -6 days in order to enter your relevant events.
For more information of how the events will be structured and ran, read here:
viewtopic.php?f=99&t=149242