If two photons collide, does the resulting particle have zero velocity?

If two photons traveling in opposite directions along the same line collide will the resulting particle have a velocity of zero relative to the rest of time space in the instant of the collision?

Photons are quantum mechanical particles. In the microscopic dimensions where quantum mechanical particles interact there are Nature's rules that dominate these dimensions, though they are usually insignificant in macroscopic dimensions.

One of these rules is the Heisenberg uncertainty principle, HUP,: one cannot define the location of a particle and the momentum of a particle with accuracy better than:

where $\hbar =6.62606957(29)×10^{−34}$ Joule second a very small number that is why it is effectively zero in macroscopic dimensions.

Thus two photons even with the same energy will not collide at a point.

Going into the mathematics of it, photon-photon interactions are very very weak, since there is no first-order interaction between two photons, but they have to go through a particle loop. In addition, momentum conservation requires two particles out.

A Feynman diagram (box diagram) for photon-photon scattering, one photon scatters from the transient vacuum charge fluctuations of the other

Feynman diagrams have one to one correspondence with calculable integrals that will give the probability for a given interaction.

A photon carries energy, two photons have an invariant mass. In their center of mass system, depending on the energy available from each, the output can be again two photons, or if there exists energy enough to generate massive particles, there will exist a quantum mechanical probability for the interaction. They are proposing high energy photon colliders, gamma gamma colliders.

Generally no, because velocity is not a conserved quantity. It is momentum that is conserved in all interactions. For photons, the magnitude of momentum is simply $$ p = \frac{E}{c} = \frac{h\nu}{c} = \frac{h}{\lambda}, $$ so photons with different energies/frequencies/wavelengths will have different momenta. If the total momentum is nonzero before the collision, it will be nonzero after.