The FCB1010 is dead easy to program. I use it stock and in just ONE bank of pedals I have: 3 presets (set up to double-tap to toggle between my two favorite scenes in each preset), two individual effect toggles, a tap tempo, 4 scene pedals that each toggle between 1 & 5, 2 & 6, etc., access to the tuner, and volume.
If I click down a bank from my main bank, I now have full access to the looper, three presets, as well as scene increment/decrement.
If I click up a bank from my main bank, I now have access to 10 individual effects.
In short, the only reason it was difficult to learn at first was because I was also learning MIDI at the same time which itself can be overwhelming. But now I LOVE it and always recommend it when people ask. Most of my posts on this forum are FCB1010-related lol! I even have a bunch of videos on YouTube about using the stock chip. You don't even need the UnO or EurekaPROM. These chips, however, have the added benefit of multiple lights on at once so you can tell at a glance which pedals are on, plus they allow you to have a momentary (hold) switch which the stock firmware doesn't allow.
In summary, yes; the FCB1010 is compatible with the III and a wonderful companion. Best of all, one can be had for dirt cheap new or used! Will I still get an FC when they come out? Perhaps. But someone on YouTube will really have to sell me on it lol!
EDIT: to further answer your question, each pedal can send up to FIVE program changes and TWO CCs. That's quite a lot of versatility. You should have no issue connecting another device; although it should be noted that you specify what channel the FCB outputs to.