I don't know if anyone can answer your questions for sure ... unless they work for Yamaha.
Having worked with the automotive counterparts to the FJR PCM I would hazard a guess that it is pretty simple and straightforward. I doubt that it has any thing considered "intelligence" or uses any fuzzy logic of sorts that might be employed in some powertrain control software to react to the driver's habits.
It is a pretty simple speed density fuel injection system with the O2 sensor feedback and closed loop fuel control. Those sorts of systems have a basic fuel map calibrated into them that is a 3D map based on manifold absolute pressure (MAP) and engine speed (RPM). Since the MAP data from the MAP sensor is pretty ragged I would guess due to short induction lengths and no plenum volume to smooth the MAP readings there is probably some sort of throttle angle factor (form the throttle position sensor TPS) that "adjusts" or smooths the MAP reading so that the data taken from the 3D lookup table for fueling is more accurate or more repeatable.
It is certainly tunable/calibratable.....but likely only by Yamaha. Unless someone has access to their code and/or has taken the time to hack into the software of the engine controller it is likely a "black box" to the aftermarket. The chances of getting into the controller are pretty slim as there are usually a number of safeguards built into the box electronics and the software itself to prevent tampering. Just my guess.
Having said that, there is always the PCIII from DynoJet that makes fueling changes quite simple. That device just intercepts the injector pulse width signal that the PCM calculates, modifys it per the map installed in the PCIII and delivers the modified pulse width to the injectors. Just as good as hacking the box and much simpler and easier and already thought out for you. You can access the PCIII with a laptop so it is easy to "adjust" the calibration per your liking.
As far as the OEM ECM changing it's map with miles or on the fly...not sure what you are getting after. The basic "open loop" fueling map that is based on MAP and RPM is not something that would likely change with mileage or time. The table is calibrated with volumetric efficiency values for each speed and load point that the speed density software uses to approximate airflow thru the engine which is needed to calculate and then deliver the appropriate amount of fuel. Those values basically do not change with the life of the engine so there is no need to adjust them with mileage or time. The closed loop fuel control (based on O2 sensor input) just modifies the open loop pulse width calculated to achieve exactly 14.7:1 air/fuel ratio to make the catalytic converter work. Possibly there is some fuel correction "learning" involved. If so, that is still not considered "intelligence" or fuzzy logic. The closed loop routine just sees how much correction it has to apply for a range of speed/load conditions and uses that correction before incorporating the short term correction calculated from the O2 sensor.
Some ECM's for some vehicles do have a new vehicle "protection" mode built into them that limits the redline for the first XX miles or reduces the spark advance for the first XX miles to reduce power output, etc. I have never seen nor experienced anything like that on the FJR although it may have something like that. Skidoo snowmobiles are known for a 50 mile spark retard that limits engine power output on their high performance engines to enable them to achieve breakin without damage from an overly enthusiatic owner. I haven't heard of anything like that on the FJR.
It stands to reason that the ECM on the 03/04/05 FJR's are the same. Likely the ECM on the 06 is "different" in that it also controls the automatic shifting transmission and clutch apply. That PCM would need to be faster possbily and certainly have far more software and more input and output pins (wires) so I suspect it is a different unit although it may be different only on the automatic. Likely the same PCM is used on both, though, with the unused pins blank on the non-automatic bikes. Hard to say without seeing one or looking at the service manual/parts list.
As stated this is just my guess to your questions as I don't have any specific knowlege of the Yamaha ECM....but I don't know if anyone will have that knowlege unless they work for Yamaha's calibration group and they will not likely post on here. LOL