There is a whole sticky thread on this forum with a ton of relevant information about booking RTWs and the value therein.

To answer some of your specific questions, depending on the carrier you book with (ie whose miles you use) the F reward gets you absolutely nothing over business. If you use CO miles and want to fly CO BF then you need to use an F award. If you book via KE or AF/KL you can get F on AF. Otherwise you can't get into any "real" F cabin. There are also some issues with how the bookings play out on domestic US routes, but I can't speak to all those permutations.

Availability is no different for RTW than it is for other reward trips, which is to say that it takes some effort and flexibility to put one together, but it can definitely be done.