Car must not change any gear in L position. And on D position there are possibly 4 or 5 gears. Usually our super genius electricians disable the last gear due to NO reason. Get these both issue checked by really qualified electrician who is expert of Auto Gears. I repeat, get it checked by ELECTRICIAN, not mechanic.
About RED Button. Look ur unable to start the car due to some reason, then definitely u have to tow or push it to near by safe place, either workshop or home or else. While the lever in P position, transmission is locked and the car won't move. As the engine is stalled, u can't move the lever to N (Neutral). Now this Red button wud help u, pressing it will disengage the lever from the transmission and ull b able to move that to N position so that u can push or tow the car