Mazda 6 Service Manual: No.2 vehicle moves in n position

No.1 vehicle does not move in d, s, l ranges, or in r position

No.3 vehicle moves in p position, or parking gear does not disengage when p is disengaged

Other materials:

Mazda 6 Service Manual: Immobilizer System
The immobilizer system allows the engine to start only with a key the system recognizes. If someone attempts to start the engine with an unrecognized key, the engine will not start, thereby helping to prevent vehicle theft. If you have a problem with the immobilizer system or the key, consult ...

Mazda 6 Service Manual: Manually Shifting Down
You can shift gears down by operating the selector lever or the steering shift switches (some models). M6 → M5 → M4 → M3 → M2→ M1 Using selector lever To shift down to a lower gear, tap the selector lever forward (-) once. Using steering shift switch (Some model ...