To confirm one of your questions: When turned the ignition switch to "on" all the lights on the IC light and then in about 2 ~3 seconds the air bag light extinguishes. ( I can't report on the TPMS light as mine is disconnected and doesn't illuminate). With my foot on the brake I can move the auto selector through all the ranges and the light/indicator on the IC follows with the correct letter, P, R, N & D. When moving the gear selector in the Drive position as when manually selecting gears it will simple indicate D; It does not follow the 1,2,3 etc selection as when you are moving down the road.
With your foot off the brake you should not be able to move the selector out of Park. Hope that helps!