Instead of the ECU using a lambda sensor to read the air/fuel ratio, it calculates the amount of air going into a cylinder using pressure, temperature and probably some stored values. It then injects the amount of fuel required to provide the A/F ratio in the given cell based on what it thinks the amount of air is.
Ok so I've been doing some of my own research and I think I was slightly wrong here. This is my understanding of Triumph Sagem ECUs to date:
The F table is a measure of how much air (mass in mg) is going into 1 cylinder on 1 intake stroke.
The AF tables tell the ECU the desired/target air/fuel ratio for a given operation condition (RPM and Throttle Position). I believe that the AF1 table is for most operating conditions and AF2 is for wide open throttle.
The ECU refers to the F table for how much air is going into a cylinder for the measured throttle position and RPM, then trims the air mass value to take into account things like ambient air pressure and temperature. It then refers to the appropriate cell on one of the AF tables to work out how much fuel is required, and thus the injector opening time.
If you want to change your fuelling you can change either the F or AF tables, but they can cancel each other out if you do both. In an ideal world the F tables accurately match the intake mass for all the operating conditions, then all you need to do is adjust the desired air/fuel ratios in the AF tables, and potentially adjust the ignition timing to suit.
I haven’t used the TuneBoy software so can’t speak for that or the manual
You should not adjust your fuelling without a wideband lambda sensor in the exhaust to give you feedback. If you are not careful when adjusting the fuelling blind you could run too lean and burn a hole in one of your pistons. You can go too rich as well, but you'd have to run it stupidly rich to damage the engine and it will run really poorly before that point. Either invest in a wideband lambda sensor setup so you can record your lambda against throttle position and RPM and make your own adjustments, or take it to a dyno.
I think I can answer more of your original questions now:
3) I believe “long term correction” is the Sagem ECU term for “adaptations” for later 955i bikes fitted with Lambda sensors, if this is correct then it shouldn’t apply to your bike. The CO value adjusts your idle fuelling to get the air/fuel ratio right at idle. It purports to be the amount of Carbon Monoxide (CO) in the exhaust but as there is no Lambda sensor it’s just an arbitrary value. You need an exhaust gas analyser to set this correctly, the desired figure I’ve seen quoted is normally 3% CO in the exhaust.
4) I don’t have a laptop to test the Windows version of TuneECU but I’m pretty sure it shows you live which cell the engine is operating in. I hooked up my phone to my bike and I can confirm the Android version of TuneECU doesn’t show which cell the engine is operating in.
5) I can’t recommend you a tune but have a look on the TuneECU website, there are all the manufacturer maps and some customs ones as well, read the notes and see which ones seem to fit how your bike is set up (air filter, exhaust etc) and give them a go. Make sure you save a copy of the current map somewhere before you start loading new maps, and reset your throttle position sensor after loading a new map.