Fishtail
It might be called shimmying.
Out of the area
To move from side to side, to repetitively change lanes.
its called rocking
Wagging
stop vehicle and see if it is dead. if so, move it to side of the road
Transverse
These are called s waves (secondary waves) while p waves move up and down s waves move side to side
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
I believe it is called a fault, like the San Andreas fault in California.
It's called the pivot joint. It allows your head to move from side to side.