Does light interact with electric fields? We know that light is an electromagnetic wave and it does interact with charges.
It contains magnetic field and electric field oscillating perpendicularly but when we apply an electric or magnetic field in any direction to the wave the applied electric field or magnetic field vector doesn't alter the magnetic or electric field in the electro magnetic wave (according to vector addition rule)....why?
 A: An applied electric or magnetic field doesn't alter the field of an electromagnetic field because, as you said, the superposition principle holds. This principle is a principle of linearity, and comes from the linearity of electromagnetic equations : there is no interaction between photons at low energies.
You can see it from a field theory point of view, as there is no bare interaction vertex between photons in QED.
On the other hand, in other theories such as QCD, gauge bosons (the gluons) carry a colour charge and can interact.
A: 
We know that light is an electromagnetic wave and it does interact with charges.
It contains magnetic field and electric field oscillating perpendicularly but when we apply an electric or magnetic field in any direction to the wave the applied electric field or magnetic field vector doesn't alter the magnetic or electric field in the electro magnetic wave (according to vector addition rule)....why?

Static electric and magnetic fields do affect electromagnetic waves, and one trusts that the mathematics works, vector additions and all. The conditions are studied in  plasmas, for example this model.
Generally, when light scatters or diffracts through a crystal the electric fields of the wave are perturbed and change direction, become polarized or whatever the conditions are. See as an example Thomson scattering for elastic scattering of light .
At the quantum mechanical level there exists a scattering of photons with  charged particles, and be assured that at the limit of the emergent classical beam the  calculations will agree.
A: In fiber optics communications, we know that when we add a new wavelength very close to other wavelengths already sending information within the same fiber (i.e. within 1 nm of each other), there is a large disruption downstream. This causes large amounts of disruptions in communications. But if we alter the electric field in adjacent wavelengths to be orthogonal to each other, the downstream disruption is significantly reduced.
This implies that the electric fields do interact.
