The long answer is that Photons are the elementary particle that mediate electromagnetic force. For the people who don't know the particles, other elementary particles are Bosons and Gluons, which mediate other forces, like weak and strong interactions. I think you know all this already so I'll move on.

So Photons are involved in Electric and Magnetic fields. They fundamentally have no electric charge, so I see the misunderstanding. I personally don't know why they're there. Maybe there was no other place.

0 charge is still a type of charge, the electronics section is fine.
(perhaps in the special section since they only move in a perfect horizontal/vertical/diagonal direction? )

That says it all.

Not really, you can make the display of a clock separate from the counter using photons though.