The RTWs are booked in a lower booking class than teh full fare F tickets, but typically in a higher than award tickets.
I do 2 to 3 OW RTWs every year. Typically it is fairly easy to get seats a few weeks out. The only problems i typically have is:
AA between JFK and LAX on the three class planes. My TA is waitlisting me and usually one seat clears, but almost never 2 wehen i travelling with my better half.
Also LA is generally difficult to get in First, especially on the SYD-AKL-SCL and sometimes for two seats on the LAX-SCL. Again, it helps to waitlist have a good Travel Agent.

And: as long as the airline has traffic rights (i believe LA has between FRA and MAD) you can book any flight operated by the OW airlines as long as they are not restricted in the rules.