[DJCarbine]

Almost sounds like the ignition/wheel lock is in a bind. Sometimes this can prevent the key from physically turning. When it happens again, try to gently turn the key while grabbing the steering wheel and turning back and forth. Does it feel like the steering wheel lock is engaged? They usually "CLICK" once you turn the wheel far enough with the key out of the ignition, which can cause issues if the wheel re-centers slightly due to the drag of your wheels on the pavement. Basically it should feel like hitting a wall while turning, and if the steering wheel is resting on this "lock/wall" you will have issues turning they key.

This doesn't explain the immobilizer funkiness, but usually what cock-blocks you from physically turning the key is a damaged key or steering wheel lock that is bound up.