Is it possible to design a helicopter with fixed rotor blades only (no blade angle/flap/pitch)?
Scaling laws are your enemy here.

Model helicopters can be controlled with changes in rotational speed, but for full-sized helicopters the energy needed to quickly change the speed of their rotors relative to the energy needed for lift creation is far too high. In detail:

The moment of inertia of a scaled-up rotor changes with the fifth power of length. The mass of the rotor changes with the cube of the linear scale, and the moment of inertia adds another factor proportional to the square of the linear scale.

A bigger object also needs slower changes, but time scales only with the square root of the linear scale. Next, the engine power available for speed changes will scale with the 3.5th power of scale*.

This still leaves a deficit of one power in the engine power available for speed changes when the helicopter is scaled up. 

Lift asymmetries in forward flight can be dealt with by adding a second, counter-rotating rotor, but scaling laws can not be designed out. As Jan Hudec points out, you need to repeat the same trick for forward-backward lift shifting, so four rotors would be the minimum to control this type of helicopter in all directions.



* Proof: Thrust must exceed weight, so thrust goes up with the third power of scale. Rotor disk area scales only with the second power of scale, so a higher acceleration through the rotor disk is required to create more lift per rotor area. If we look at the power required in the static case 
$$P_{min} = \frac{\eta_{Prop}}{T_0}\cdot\sqrt{\frac{\frac{4\cdot T_0}{\pi\cdot d^2}\cdot g}{2\cdot\rho}}$$
and insert the scaling factor in all scaleable variables, a power of 3.5 remains for the minimum power $P_{min}$. This is more than the increase in static thrust because the efficiency of the rotors declines with higher disk loading.