DOnt worry too much about 1-3 psi difference dude. The tyres temperature is always up and down , and that can create that. If you want a constant tyre pressure get it fill with nitrogen.
I dont think stock ecu has the self learning capability after you reset it or whatever. Unless if you got piggy back ecu or stand alone ecu then you can notice the difference in power gain after you dyno tune it.
I came from NZ and my mum import her private car to sydney. Car needs to be purchase for at least a year ( under the old rules ) and you need to live in NZ for a year too.