Is light reflection or any other reflection a type of force?

When a photon interacts with an atom, three things can happen:

1.elastic scattering, the photon keeps its energy and changes angle

2.inelastic scattering, the photon gives part of its energy to the atom and changes angle

3.absorption, the photon give all its energy to the absorbing atom (and electron)

Now in your case, reflection is 1., elastic scattering.

You are correct that the photons for example when they interact with a mirror's lattice's atoms, and get reflected (elastically scattered) they excerpt pressure on the mirror. So as you say they create force, by excerpting pressure on the mirror in the direction of incidence.

Now you are saying that reflections are types of forces, but in reality during a reflection, total energy is conserved. The photon changes direction and part of its momentum is transferred into the mirror's atoms' or molecules' kinetic energy and thus excerpting pressure on the mirror.

Reflection itself is not a force, but these forces are involved, and since this is an EM interaction between the atoms and the photons, the force mostly involved is the EM force (of course the other forces are involved too, but those effects should be negligible).

Force is a change in momentum.

The momentum of incoming photons in a ray is in a different direction than of those outgoing an instant later in the reflection of that ray. Therefore, you could say there's a force on the ray. There's a reaction force on the mirror. Light shining on a mirror pushes it away.

However, when one photon bounces off a mirror, it's technically a different photon going out than the one that went in. In quantum mechanics, we consider the incoming photon to be destroyed, and the outgoing one to be created. So it would sound odd to say that a force acted upon the photon.

If you are asking if a force is involved in the reflection of light from a smooth surface, then the broad answer is yes. Photons carry momentum proportional to the angular frequency of the light they compose: $p = hbar omega$. When a reflection occurs, part of the photons get a kick from the mirror and change their direction -- implying a force is involved. This is akin to any material object bouncing off a surface. For instance, if a light beam strikes a mirror at $45^{circ}$ to the normal, each photon that gets reflected suffers a $sqrt{2} , hbar omega$ change in its momentum in magnitude. Note that I've assumed elastic scattering, where there is no loss of energy for the light.