For a Gen2 FJR, you must get a PC5. A PC3 from any other bike, including a Gen1 FJR, will have the wrong connector for your wiring. Also, if you want to do the job properly, you need an Autotune unit with a new O2 sensor to go with the PC5. Without the Autotune unit, any map that you program into the PC5, will only tune the engine for one particular set of atmospheric conditions. When those conditions change, as they will due to temperature, pressure, altitude, and humidity, there is no feedback loop to re-tune the engine.
Yes and no...
You can get a used PCIII that was set up for an GenII FJR - it will work fine. Dynojet just replaced them with new units - the PCV. The AT module will only work with a PCV.
The ECU has maps specifically to adjust for temperature, pressure, altitude, and humidity - you don't need an AT to compensate for those changes. Running without an Autotune will mostly work fine. You will probably end up with the mixture being slightly off when you go from E10 or E15 back to real gas without an AT.
An AT is useful for mapping for the specific changes made to your bike. I have an AT and the bike runs a bit smoother than just running the "smoothness" map. The AT doesn't seem to work well below 3k rpm and 10% throttle on my bike, however. It richens everything up and then leans it down again, leading to inconsistent running. If I was doing it again, I'd save the money on the AT.