Sounds like battery is OK. Codes are 12 - Crankshaft position sensor, 14 - Intake air pressure sensor (MAP sensor), 30 - Lean angle sensor. An actual fault 12 or 30 prevent the bike from starting, MAP sensor won't.
Since it does start occasionally, you perhaps have an electrical gremlin. Gen2 has ground spiders, and my guess is those codes are intermittent due to an intermittent connection..... more like a common ground or earth as you call it. I'd recommend checking S4 first as it carries the most grounding load. It is located in the engine compartment.
While you're in there, you can unplug and re-plug the crankshaft position sensor (on valve cover, right end, connector at throttle bodies). MAP sensor hose can get crud in it, two screws to remove, clean any crud on the vacuum nipple and ensure the hose is clean throughout... it will cause poor running.
FJR's don't like to be started and shut down without warming up sufficiently, fools the ECU into thinking it needs more fuel at startup, thus too much fuel. If that happens, hold the throttle wide open while cranking in say 15 second bursts... A good run up to operating temperature will clear the condition.
As for the codes, I suspect they are false, so clear them and see if they come back. Again, I suspect an intermittent common ground to start with....
If you have ethanol fuel and bike has been sitting, an ounce or two of isopropanol or fuel system conditioner containing isopropanol (Seafoam) will take care of any water that may be sitting at the bottom of the tank... only takes a couple of tablespoons to prevent the bike from starting or running well (can't run on water). If it runs poorly when you go for a ride, this or the MAP sensor hose plugged may be the cause.