Plenty of Q's here...
Gear selection could be a few things, first thing to check would be air in the lines maybe, or duff slave cylinder seal.
Neutral light is more than likely going to be the switch, either faulty or needs adjusting, as I've never had your model of bike I can only guess it would be the same as the 916 variant, you should see two wires going into the back of the engine on the clutch side, that's the switch.
Finally tyre pressures, well that's down to the rider, bike, tyres, weather and riding style more than anything