Theres a switch 2 buttons to the left of the defroster switch. That switch is to raise and lower you head lights without turning them on so you can change the headlights. The switch could have a short in it causing it to act like that.
The burning smell indicates a short in the electrical system somewhere. I would start by replacing the headlight switch. If that does not work you will have to have a mechanic look at it.
If you turn up your interior dashboard light settings, then the radio display will be brighter too. The radio dims to the setting for the dashboard when the lights are turned on.
The parking lights are turned on when the headlights are on and you pull out on the light switch. The parking lights cannot be turned on by themselves.
The middle two lights should be on when you turn on the headlights.
there should be a button by the steering column that enables you to bypass the motor in the pop up headlights. Try pressing that and see if they go down.
Break lights come on when you step on the break, they do not come on when the head lights are turned on.
Because you have to eat french fries with ketchup!
the dash and radio lights are supposed to dim when the headlights come on. Make sure you have the brightness of the dash lights turned up as much as possible.
Perhaps you turned on the interior lights when you were adjusting the headlights?
Brake lights should NOT be effected by the headlights. Brake light function is completely independent of the headlights. Assuming you are not refering to the tail lights, or marker lights, which are supposed to come when the head lights are turned on. Not having brake lights when the head lights are on is a big safety problem and should be corrected.
I would replace the headlight switch as Ford has had their share of these problems.
It may be wired wrong.