Light and Gravity 
The gravitational force does not affect the speed of light rather affects the frequency of light (hence light changes colors, red to blue and vice-versa).

I know this has been verified but I have 2 questions:

1.Why the speed of light is not accelerated due to gravity?
2.Why the frequency is affected? (if the energy has to be altered, then instead of frequency, wavelength could have been changed)

 A: Anything with mass and/or energy warps space-time. When Light with different energy level passes through gravitational field of a massive object, higher energy will be attracted under the influence more than lower energy light. But, Higher energy of light particle will have more inertia than low energy particle. And since light of different energy level travel the same speed (or escape velocity), they follow same shortest possible distance from centre of object (let's say galaxy). Light of different wavelengths feel same amount of acceleration from galaxy centre [a= F(c^2)/E. so blue light feels more pull (F)but has higher energy (E)]. Since acceleration due to pull is same, Light is deflected by same angle, independent of colour of light. the interaction of light with massive object results in exchange(or loss) of momentum. Hence, gravitational redshift.  According to a= F(c^2)/E (Here, C=constant, and E=hf), it naturally depends on frequency of light. This is result of GR theory. 
However, to reconcile GR with Quantum Gravity, Many alternative theories have been proposed and one of them is Rainbow Gravity. The theory postulates that Gravity affects different EM energies are differently much in a same way as Prism.
So, blue light should hold little longer around this massive object than red light and consequently deflected more. 
A: The laws of special relativity, of which the constant speed of zero mass particles in vacuum is a basic tenet , have been tested innumerable times with many experiments, particularly in particle physics. The Michelson Morley experiment has shown that there exists no luminiferous ether, i.e. there is no medium on which light propagates with this velocity c. If there were a medium it should obey Lorenz transformations , keeping the velocity as c.
The quantized nature of electromagnetic radiation is equally well established, giving an energy to photons h*nu where h is the Planck constant and nu the frequency.
General relativity in its theoretical framework, incorporates special relativity. This means that the velocity of light in vacuum is a constant in General Relativity too, impsed in the mathematics.
Thus it is the mathematics that predicts that photons, since they carry energy, have to be affected by the gravitational fields, and that this effect will manifest in the energy of the photons affected. This prediction has been verified by observations, from star and galaxy systems to solar radiation.

All the observations have resulted in  a coherent cosmological model, consistent with the observations, i.e. validated.
Please keep in mind that gravitation from Newtonian physics will not "see" a zero mass particle at all. The fact that redshifts to the known spectra appear when the photons pass a strong gravitational field is expected in General Relativity.
