I don't think that's correct. Electricity is the electron potential across a medium. That's not the same as an electromagnetic wave.

Yeah, it is correct. The electromagnetic interaction is mediated by the photon. An electron is just one of the fundamental particles that interacts electromagnetically. We use free electrons in metals for the conduction of electricity, but in the end all the interactions between the electrons, protons, etc are governed by photons.

If you want to learn more, something to google would be quantum electrodynamics. There are some nice introductory talks about it, but be warned. In order to really understand this, you'll need to study physics, more specifically quantum field theory.

The reason there is a potential is because of electromagnetic forces, which are mediated by photons. It’s a bit complicated.

What? Give me a link so I can learn.

Trick question (or trick answer): depends what you mean by "electricity", which is one of those questions that's simple to ask but collapses into a pile of details on closer inspection.

The electric field and magnetic field are tied together in the manner described by Maxwell's equations. This results in "electromagnetic waves", which are indeed carried by photons in free space.

It is often helpful to look at the fields as being the real "electricity", or at least use the lumped approximation we call "current", and this brings various charge carriers along with it. Electrons are the common charge carrier, but ions can carry charge (e.g. in batteries), and in semiconductors we use "holes", which are the absence of an electron. Not an anti-electron, just the space where it's supposed to be.

So the first paragraph on the photon wiki page might give you a start: https://en.wikipedia.org/wiki/Photon