I just don't understand people's main concern when buying a second hand car is repair bills. Any old car will have them, only way to avoid them is get a new car.
All I can tell you I used 20/50 in my 400's, 5/30 in the 430 and 0/20 in the 600 without any problems, though I wonder if 0/20 is too thin for long distance driving.
Turn off ignition and change as normal. The plug you are referring to is the hybrid battery. Do not unplug. You could jump start the car and recharge it as normal.
Owners maunal page 287. Lexus not designed for towing. I am not sure if they said the same about the 400. I got a tow bar made for the 400 and bought a tow bar from Lexus for the 430.
I had 235/50/18 on my old Ls430 with out any problems. I tried 55 on the back, they rubbed with a load on some corners. Tyre fitter said 55 would not fit on the front.