hey gootah, welcome to the forum!
MIDI controls for the Axe-Fx are definitely much more straightforward once you have one to mess with.
I'll try to explain briefly though.
The eight "external controllers" supplement the existing internal Axe-Fx controllers: the LFOs, ADSRs, Sequencer, and volume Envelope.
Each of these controllers can attach-to/modify select parameters on the effect blocks (and elsewhere, but mostly on the effect blocks).
So you can have an LFO modifying the frequency of a wah, or a sequencer modifying that frequency, or have the frequency vary by input volume, or...
use one of the eight external controllers.
The eight external controllers are each assigned a MIDI CC number. Whatever MIDI CCs the Axe-Fx receives that correspond to whichever of those eight controllers you've assigned to those CCs... the value of those CCs gets sent along to whatever's being modified by the corresponding external controller. (Feel free to read that again! It's weird enough to write it out!
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Additionally, and sometimes missed by people who don't have an Axe yet, *every* effect block can have a CC assigned to it's bypass function. So you don't need to waste any of the eight external controllers turning effects on and off. Add to that, more CCs for two bypass states, five different volume adjustments, tap tempo, activating/deactivating the tuner, and looper controls (on the Ultra) -- you've got the majority of things covered. And then to supplement that, the two 1/4" pedal jacks can also be used the same way as all the other controllers noted previously, along with a couple of other pedal-jack-only functions.
In short, the "External Controllers" are there for MIDI-based expression pedal style control.
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As far as what MIDI is sent out... not much, actually. And at the same time... just about everything.
If I'm remembering right, the Axe never sends CCs or PCs. However, it does use proprietary messages via MIDI SysEx to send out nearly everything that's going on. Applications or hardware that can understand those messages (Axe-Edit, the MFC-101, the Gordius Little Giant, and the Liquid Foot among the most well-known) can then react to those messages and, for example, display the tuner and tempo data from the unit.
Hope that helps!