congrats with the buy! ;)
1) normal, no riding = no wind => forced cooling with fan.
2)a. don't know what you mean with the lurchy & lean stuff (shoot me, i'm european :D)
b. normal, this happens when the engine is just in compression stage. i use an optimate battery loader when i don't use the bike for more than a week.
3) best result is a remap, second is a race ecu and 3rd leave it as is.
all depends if you're buying the pipe for performance or sound.