Is it important for a system of two or multiple particles to have internal force acting on them? While studying the concept of center of mass, i read about internal forces as the force applied by particles of a system on each-other but is it necessary for all systems to have internal forces, can there be a system of several particles with no internal force acting ? 
 A: Low energy photons are massless and chargeless, and you can in principle have a system of low energy photons that don't interact via any internal forces. So that's one example.
A: 
can there be a system of several particles with no internal force acting?

I suppose all particles have some form of interaction (at the very least gravitational), but there are many scenarios where this can be ignored. For example, when treating a system of particles as an ideal gas, we assume the particles are non-interacting (other than the occasional elastic collision, but otherwise we assume no interactions).

s it necessary for all systems to have internal forces?

No, it isn't necessary. The only time you should consider the internal forces of a system is if they are actually present and relevant for the analysis you are performing.
A: 
Is it important for a system of two or multiple particles to have internal force acting on them?

The photon example is a good example of particles existing in a "system" without interacting with each other. But they do not form a bound state, because of this. In addition to have a continuous "system" with photons one needs the photons interacting with matter, as for example in this video here. .
So it depends on your definition of a "system". 
For sure particles that have no forces between them cannot form a system of bound particles.
