Can a helicopter fly with just one blade? I read somewhere that the main helicopter body will also spin in the opposite direction to maintain angular momentum, is this true?
 A: Yes, without a means of counteracting the torque caused by the main rotor, the helicopter will rotate pretty much uncontrollably.
There is plenty of footage on YouTube,  if you have the stomach to watch it, of what happens when the tail rotor fails.
How Helicopters Fly gives you more details.

Image source: Driemond fire department.
If the tail rotor failed on the above helicopter, it would spin in the opposite direction as a consequence  of the law of conservation of angular  momentum.
One method of recovery is to immediately shut off the engine, and allow the helicopter to autorotate which, although disorienting to the pilot, will reduce the spinning of the helicopter body.
From Autorotation

If the tail rotor fails in flight, engine torque can no longer be countered by the tail rotor, and uncontrolled spinning of the aircraft is a possibility. Most manufacturers call for an immediate autorotation.
An autorotation is a natural way to deal with an inflight tail rotor failure since it reduces torque to zero. One problem with an autorotation is that it will be difficult or impossible for the pilot to align the landing gear with ground track during touchdown.

