is it possible that an airplane could fall down due to severe turbulence?

yes

YEs very much.atleast in LOST

yes, it's called a downdraft, but they are rare, enjoy your flight .

A wing makes air travel faster over the top of the wing than the bottom. This creates a vaccum on the top of the wing which in turn creates lift.  Turbulence can make this a difficult task.  No lift means heavier than air objects sink.   An airplane with no lift fits that description.

It would only cause a slight fluctuation in altitude and a very rough ride. Only a severe tail wind or microburst would cause a plane to fall out. The NOAA flies into hurricanes all the time - severe turbulence and no accidents. They fly into the wind not with it (tailwind) otherwise that would end with devastating reults.

Hmmmm? Well, hard to say, depends I guess on the type of turbulence. Airplanes gain Lift from the Design of their Wings. The propeller, in a simple explanation, Provides an Air Flow across the Wings buy pulling the plane through the air. IF, turbulence was in the form of a Strong Tail wind, or Vortex (Tornado motion), updraft, downdraft and exceeds the forward motion of the pull of the propeller or lift, then the plane could possibly fall (Stall). When a plane reaches the minimum forward motion a Buzzer goes off to warn the Pilot that He/She has lost the needed forward motion for Lift. Hopefully, a person is skilled in this problem to regain Lift and NOT fall. That the easiest way I can explain without getting very Techinical, maybe someone can say it better.

The "falling" feeling you feel in reality is the aircarft moving only a few feet up or down from it's altitude (like a quick elevator ride). In bumpy air, a downdraft can momentarily cause altitude excursions.

Turbulence, is the leading cause of nonfatal aviation accidents but turbulence alone rarely causes an fatal accident. Additional weather factors usually are the major cause, while turbulence is just a contributing factor.

"From 1992 to 2001, there were 4,326 weather accidents that occurred in the United States. Of these 4,326 accidents, 509 were cited as turbulence weather events. (Not all accidents resulted in a crash.) Nearly 23 percent of these turbulence-related accidents resulted in fatal injuries to the occupants of the aircraft. The National Transportation Safety Board (NTSB) cited downdraft as the cause or factor most often in the general aviation accidents. Clear air turbulence was cited most often in the air carrier accidents."

http://www.nasdac.faa.gov/aviation_studies/turbulence_study/turbulence_study_new.pdf

Here is a listing of accidents where turbulence was a factor- http://aviation-safety.net/database/dblist.php?Event=WXT
You will find that most were the result of operating in weather that was far worse than simply turbulent air.