1. The steering wheel tends to shake when I apply the brakes. And I feel the car lightly shaking back and forth.
The tire bounces and the suspension is weak and just keeps bouncing.
The pulsations are most likely the thrust arm bushings.
OE was rubber and if sags it can cause the steering wheel to pulse 2 inches on brake application. Most use eurothane bushings that never need replaced. BMW came out with the 750i bushings requiring the installer to grind the bushing down to fit.
Here is a link to Paul Gray, Grunt, who makes a replacement for this bad deal. http://www.gruntsbushings.com/index.html
Thrust arms with new bushings installed.
2. When I was driving last night, the headlights shut off on a few occasion.
Replace the k4 low beam relay.
3 and finally, when I am driving everyone now and then I hear a light high whisper.
I have no idea what you mean.