Okay first of all, I would not use a BSP for the doors. Try using blueprints and model some simple shapes. Here’s a tutorial on how to open a door via blueprint and a brigger volume:
And here’s one to create a light switch:
this seems counter intuitive at first, but if you understand both of them you should be able to use that knowledge to build a switch that opens your door. 
And that’s basically it, try to find tutorials that do part of the stuff you want to achive and combine it in a way that suits your needs.
As for your second question. You might want to take a look at this tutorial series:
It sounds like you need some kind of AI to do what you’re trying to do here.