This is probably the most noobish question ever, but I've only been at this a week, so go easy: 
I take it then, that brushes can't be cut up and remain as one brush, right?

My first attempt at a single door leaves me with 7 brushes. It's just bothering me that there's all those extra polygons running through the middle of the wall that will never be seen. Is there not a more efficient method?
God forbid if I want to do something like this:


carve.
I rarely use clip and never carve. the primitives plus vertex manipulation alone is enough to get me any shape I want. BSP doesn't like lots of adding or subtracting so I don't even clip if I can avoid it. To be honest, vbsp tries its hardest to delete all the faces you can't see and nodraws, so it doesn't matter if you end up using more blocks as long as your map doesn't leak.
