Are you trying to shift it into 4 LOW?? If so, you have to be rolling 2-3MPH. Check your owners manual.
Yes. It would be illegal to advertise them that way if they were not. Though some have the ability to switch between 2 and 4 wheel drive.
Most vehicles need to be stooped and in neutral before they will engage the the 4WD in low.
No.
Could be the 4x4 Control Module.
Turn 4WD off. Put transmission in reverse and back up a few feet. Return transmission to drive. If this does not work then something is not right and you should probably take it to a shop. Answer...