Ausatco,
In answer to some of your questions, I can give you some info with regards to LAX airport - although I haven't been there for a few years now.
The airport has two sets of parapllel runways in a north/south complex arrangement. One of each set of runways is usually used for takeoffs and the other runway is used for landings.
On first contact with tower, you are usually cleared for landing - presuming the conditions are VMC (which they usually are in LA). It is then up to the crew concerned to ensure that the runway is clear before landing. When conditions are IMC, things are a little more interesting. I only experienced one go-round at LAX and that possibility was pretty well advised early-on by ATC. The rest of the time it works reasonably well - although it does rely on everyone expediting their approach and occupying the active runway for the minimum ammount of time. Also, arrriving aircraft were often told to hold on the crossing taxiway and were then cleared enmasse to cross the takeoff runway when a gap in the sequence occured - a real Le Mans rush!!