1. What information do photons carry?
None I think. Photons of specific wavelengths and/or energies can be measured and scientists can deduce what the photon came from (i.e. certain substances always emit light of a certain color…in this way scientists can determine what a glowing object is made of). Likewise, a certain pattern of photons can carry information as through a fiber-optic cable. However, I don’t think you can say a photon itself carries information.
2. How do photons originate?
Just above I mentioned that a photon could tell someone what it came from by measuring its energy/wavelength (remember light can be considered both a wave and a particle simultaneously). Atoms have electrons orbiting them. Different types of atoms (hydrogen, helium, etc.) have different numbers of atoms ‘orbiting’ them in different shells. The electrons cannot be just any random distance from the electron but MUST orbit in prescribed distances from the nucleus (center) of the atom. If you add energy to an atom you will excite the electron. If you provide enough power for the atom to jump to the next level it will…anything less and it will stay put. However, the atom doesn’t want to stay at the higher energy level and prefers to drop back to is ground state. When the atom drops back down a level (or two or three or whatever) it emits a photon of light. As I mentioned each type of atom is unique in what levels atoms can orbit at. So, when something emits light of a particular wavelength you can determine what it was that made that light.
3. How is a photon destroyed?
Photons are being destroyed all the time. Look at your desk…it’s happening right there. White light hits your desk and it absorbs all wavelengths except a few which it reflects. This reflected light determines what color you perceive your desk to be. The absorbed photon gives its energy to the desk causing your desk to heat up. Of course, there isn’t enough light in your room to significantly heat the desk but it is happening just the same.
As for the electron its anti-particle is a positron (not a photon).