Insert the key and doesn't turn. Steering wheel locked. Shifter stuck in park. Can start by mechanical part under wheel. What could it be?

1999 ford f150 won't come out of park or start even when I start it using the mechanical part under the steering wheel

Needs to be adjusted by a certified Ford truck technician. It shouldn't cost an arm and a leg… But it SHOULD be that certified tech - anyone else is liable to screw it up worse than it already is!

You can usually get the key to turn by moving the steering wheel back and forth while you turn it.

That's usually typical of a vehicle parked on a slope. The weight of the car on the parking sprag in the transmission tends to lock it up and if the steering is slightly off center when the vehicle is shut off it will lock up also. I have it happen to me many times in my sloped driveway. Just work the wheel back and forth slightly while turning the key and it will clear the problem.

The VAST majority of the time, if the correct key won't turn in the ignition, you need to turn the wheel slightly.
If that doesn't work for you, you are PROBABLY using the wrong key.

Note: The key DOES NOT have to be in the run position to replace the ignition lock. It is just easier to remove the existing lock with the key in that position.

Can start by mechanical part under wheel.
That part does not exist. If it did, the key wouldn't be needed.