If photons (zero rest mass) have no anti-particle, do Particle / Anti-Particle pairs necessarily have rest mass ? For example, that Anti-Neutrinos exist demands that Neutrinos have rest mass ??

Gluons and photons need not have mass to be considered their own anti-particles.

Two photons can and do extinguish themselves to produce a pair of electromagnetically charged particles when the center-of-momentum energy is high enough. This is usually called pair production and not photon annihilation.