Hi there, welcome to LOC! :)
Just to get you started, first of all the IS200 Sport was never available as an auto, only the S and SE came with an auto option, the Sport was manual only.
Engine-wise they are all identical, all 2ltr straight 6 with 153bhp. However as the manual is a 6 speed and the auto a 4 speed the manual is quite a bit faster - the manual does 60 in 9.something while the auto takes 11.2 to 60 (although I do agree it feels faster than the numbers might suggest)
The PWR button simply makes the throttle a bit more sensitive, and makes the gearbox change up later and change down more eagerly, basically just makes it more responsive - unfortunately makes no difference to power whatsoever.
Nice that you seem in good spirits but sorry to hear that you've lost a leg, glad you're enjoying the new car.