Light on refraction

What happens to the wavelength and the frequency of light on refraction?

Compton Effect in light which dealt with collision between photons and electrons provided the energy was in the right range.

In the collision between the photon and the electron the photon loses energy and its frequency lowers. How is refraction very different from this? refraction taking place from less denser to more denser medium, so the photon came from a space where there were fewer particles to collide and is going into a place where there are more particles to collide and there are almost no reasons why collisions must not take place, so the photon should lose energy and hence get a change in frequency too.

Nothing happens to frequency, wavelength and velocity changes.

What makes scattering, refraction and dispersion different? Aren't they interactions og photons with the medium, fundamentally?

Refraction has nothing to do with Compton Effect. In refraction the scattering is elastic and hence the frequency doesn't change. The effect of scattering is seen macroscopically from the fact that the velocity and the wavelength of light in the medium has changed.

If in my medium the particles were initially at rest. Now if I let an electromagnetic radiation pass through the medium in proper terms refract through the medium then also the final state of my medium should be at rest.

Consider a photon absorbed by an electron and then re-emitted with the same energy in some other direction. This is what happens in case of refraction as well. This is elastic scattering. Such scattering of photons effectively reduces the velocity of photons like electrons in metals.