What makes recoil? is it the bore sizes or poweder, velocity or what?

The amount of gun powder usually has some affect on how much recoil it has. But it is also Newtons 3rd law, every action has an equal and opposite reaction. Barrel length has nothing to do with it, neither does velocity.

Its the force of the bullet and gases being forced out of the barrel.

every action must have an equal and opposite reaction.

The explosion forces the bullet out.  More precisely the explosion forces the bullet and the gun apart.  The force operates on both the bullet and the gun.

It is simply conservation of momentum.
the shot moves forward with momentum m * v  and the gun must move backwards with the same momentum.

Now for any given amount of energy, the lighter the bullet means that it moves faster but it actually has less momentum.
Modern rifles with a light high speed bullet give a lot less recoil than an old fashioned blunderbus for example.

As the gun moves backward with the same momentum, a light gun will have a higher speed and a more sudden kick.  If all else is the same a heavy gun moves back more slowly.  The result is a more gradual push rather than a sudden kick.

Given that impulse = change in momentum  F*t = m*v
if the gun moves back more slowly the time of the push is greater and the force on the shoulder is less.
Even if the the momentum was the same.

All the other factors you mention are only relevant if they affect the momentum of the bullet, or the mass of the gun, or the time that the recoil is distributed over.