It might be called shimmying.
Out of the area
its called rocking
To move from side to side, to repetitively change lanes.
Wagging
stop vehicle and see if it is dead. if so, move it to side of the road
Transverse
It's called "ramming another vehicle". The terms you are probably looking for are "sideswipe" when you scrape along the side of another vehicle. In stunt driving, one car ramming front first into the side of another car is called the "T-bone" (for the obvious similarity).
Start point
It's called the pivot joint. It allows your head to move from side to side.
The tip of the nose that can move from side to side is called the nasal tip cartilage. It is flexible and can be manipulated slightly, allowing for some movement and adjustment of the shape and position of the tip of the nose.
In a head on collision, they will be thrown forward in each vehicle.