Although photons don't have a rest mass, they do have momentum; and this means lasers have recoil by Newton's Third. However, the effect is tiny.
Regarding photon mass, there are two ways of looking at it once of which is more useful than the other. First, a zero rest mass with an infinite tau factor (from relativity) leads to an indeterminate result. 0x∞ = ?
Second, and also from relativity, energy and mass are interchangeable. Since a photon has definite energy (at least somewhat definite; quantum mechanics and Heisenberg uncertainty chime in here) that means it has a definite mass while it's in flight. It turns out that photon momentum is equal to h divided by the wavelength, where h is Planck's constant