What will happen when photons moving in opposite directions collide?
Photons appear to mostly interact as waves rather than particles so I think they don't actually collide as such, although there is some weak scattering of light by light in a pure vacuum.
This is a very complex subject and the answer is probably not fully understood yet. It certainly is not by me. However I'll do my best to give a limited answer.
Photons are a way of describing what we know of electromagnetic radiation and they appear to behave in similar ways to both waves and particles (as quantised packets of energy).
They generally interact with each other in the same way that waves do, refracting, reflecting, cancelling when out of phase and reinforcing when in phase, etc
I think they pass through each other as waves do rather than collide as particles do, although there is some weak scattering of light by light in a pure vacuum if the intensity is high enough.
Extremely high energy photons can interact to form other sub-atomic particles (e.g. an electron–positron pair) although this is not exactly a collision as an interaction in which energy is converted to matter I think (