Photon photon scattering is a thing [1] but I am not sure whether that is implied by the interaction of light and electrical charged particles acting both ways. I slightly tend to think that is not implied but I am not a physicist.

[1] https://en.wikipedia.org/wiki/Two-photon_physics

Interesting! Thanks

Yes, they are. They cannot interact directly, but they can via "virtual" electron/positron pairs (or actually any other pair of charged elementary particle + antiparticle).

To expand a little -- the process is known as light-by-light scattering.

Searching will turn up plenty of good references, like this one: https://home.cern/about/updates/2017/08/atlas-observes-direc...