There's an FAQ on the official organizational website http://www.narcoa.org/
and both of these questions are answered.
They rent the track for events and usually events are scheduled during no traffic or light traffic times. If they meet a train, it is the same as 2 trains meeting, and one (usually the hobbiests) sits in a shunt track while the other passes.
The railroad companies help coordinate things.
All in all, it sounds like a fun hobby. But I've got enough expensive hobbies at the moment.