BSP Tree Questions

Hey guys, I've just been doing some readings on BSP tree on the net and have a few general questions about them.

1. There were a few articles/tutorials that I was reading on partitioning the geometry, but they really weren't clear on ways to do it. In a few of them, they said just to choose one piece at random and partition that way. But to me that wouldn't lead to a balanced BSP tree. So what are some other good ways to divide the space so its roughly balanced? Or would it be better for the geometry creator to partition it manually for best results?

2. I can see how the BSP trees can be applied to seeing if a collision happens between walls of geometry, but I can't see how it would help for ground collisions. So do we have to subdivide the geometry in another way to see if there is a collision with the ground? :confused: Or what?

3. This kind of relates to question 1. When subdividing a plane, we have to find the plane/plane intersection line and find the endpoints of the line. Do we replace the plane with the 2 new planes in the actual geometry, or do we just add the new planes to the BSP tree and leave the geometry unchanged?