> Also, do other particles behave like this?
Yes, as you note, photons are their own antiparticles.
The maths doesn't have a preferred time direction, so two photons can annihilate into an electron-positron pair.
I'm not sure if this has actually been observed given how hard it is. That said, my favourite type of supernova is caused by pair creation, though I don't know the proportion of that which comes from 2-photon interactions: https://en.wikipedia.org/wiki/Pair-instability_supernova
There's also Majorna particles, but as I understand it the only known particles that are definitely Majornas are also quasiparticles: