Encoding:
Information can't be "transferred to a set of photons (with no mass) and hold varying "states" within the analog light". The photons themselves do not store/carry the information inside them, but the variations in the number of photons (flux, intensity), or the variation in the frequency of photons can carry information.
"Constituent state of matter (and the "states" represented by them) in a circuit" are (usually) just varying voltage levels. These voltage levels can be converted into varying light intensity or varying frequency by various devices (the most widespread are LEDs and lasers). Thus, the (digital) information present in your circuit can be converted into light using relatively simple schemes - just turn the light ON and OFF in some predetermined manner (e.g. Morse code as suggested by @Passerby).
Radio waves, on the other hand, is all about sinusoidal signals. Yes, from theoretical point of view one can think of light and radio waves as being the same, but this approach does not work in real world. You can not transfer "digital radio wave pulse" wireless - you must send sinusoidal signals. If you are bound to use sinusoidal signals, then there are three parameters that you can change in order to encode your digital information: amplitude, frequency and phase. This encoding is called modulation, and it is very large topic (with many mathematical aspects).
Note that even though you can send digital information over light without employing modulation schemes, there are cases where the light's intensity or frequency may be modulated with digital information. The reasons for this complication may be: higher signal's integrity, higher SNR, higher bit rate and many more (the table applies to communication over fiber optic only):
However one of the most important advantages of modulation (maybe even the most important one) is that modulation allows for sharing a single physical media (both wired and wireless) between numerous logical channels. For example: phone, internet and TV can be "delivered" in parallel (simultaneously) over a single optic fiber cable when appropriate modulation scheme is used.
Decoding:
There are electronic devices which convert varying light's intensity or frequency back to varying voltage levels (the most common are photodiodes and photovoltaic cells). Once your information is represented by voltage levels, you're back in the usual electronics design. Various demodulation schemes may need to be implemented, depending on the modulation schemes initially used.
For radio waves the same is true, but the received signal is a modulated sinusoid, therefore demodulation schemes are always used. The device which receives radio waves and converts them into voltage levels is called "antenna".
Your question rests on a few misconceptions, but it's still a good question.
First, since electrons have negative charge, their actually pushed from the point of lower electrical potential towards a point of higher potential.
Second, we don't normally think of a single electron travelling all the way through the resistor. Many many electrons exist in the material to begin with. When an electric field is applied, they're all pushed together towards the higher potential. Some of them are free to move and so they move.
In fact, the electrons that are free to move are mostly already moving, randomly in different directions. When the field is applied, it just tends to slightly skew the distribution of their direction of motion so that the overall trend is for the electrons to be moving toward the higher potential.
But along the way they're likely to interact with atomic nuclei or other electrons and bounce around, resulting in the randomized motion we just discussed.
Each time an electron "bounces" off an atom in the material, it can give up a bit of its kinetic energy to the atom, and set it vibrating. This vibration can be transferred to the other atoms nearby, and the overall combination of different vibrations is what we experience as heat.
As for whether the electrons that come out the far end (the high potential end) of the resistor still have some kinetic energy (and electrical potential energy), yes they do. And they continue to experience resistance as they (roughly) travel down whatever wire connects them to the + terminal of the battery. But the resistance of the wire is (if the wire is chosen correctly) so small compared to the resistance of the resistor, that we can ignore it for most purposes.
Best Answer
I do not believe the active users of Physics SE are patient enough to write or read explanations that can be understood by most of us - the practical electricians. I write an answer here.
Elementary concepts such as "radiation is emitted when electron returns to lower energy orbit" unfortunately explain too loosely what happens in solid materials.
At first solid conductive material doesn't have some sparse allowed electron orbits. When interatom distance is small enough atoms disturb electrons in other atoms, the number of allowed orbits is vastly increased. A part of electrons move in so complex orbits and long distances that they are practically free in the emptiness between the atoms when compared to electrons in tighter lower energy orbits.
Atoms attract indirectly also each other when many atoms attract the same electron. This keeps the material solid - the distribution of the electrons between atoms happens to be a total energy minimum.
The number and variety of the possible electron orbits is so huge that only statistical distribution calculations are possible.
So, what makes electrons to jump from lowest energy orbits to the numerous free upper energy orbits which are possible in solid materials? Thermal excitation, they say. What's that? It's the mechanical thermal motion they say - random vibrations which cause thumps also to electrons.
But there's no such thing as mechanical thump. Electron can change it's course to higher energy orbit ONLY by absorbing a photon and to a lower energy orbit by emitting a photon. When do these things happen depends on are free orbits available, is there radiation available to be absorbed and the life statistics. Electron stay in certain orbit a random time which cannot be determined. Only statistical analyses are possible. That's one basic facts of the quantum physics.
Atoms can vibrate around their equilibrium positions - that's what the heat is. But all inter-atom thumps are relayed by the common electrons. Together with the previous paragraph that means the material is full of radiation - photons. Physicists handle photons as gas which obeys certain statistics. It's not the same statistics as particles obey because photons born and vanish all the time due the state transitions of the electrons. But their statistical nature is theoretically derived and it explains at least one phenomenon very well: All the time some photons escape out of the surfacea of solid materials. Those photons you already know. It's the thermal radiation, mostly at infrared wavelength range in temperatures that we humans can stand, but also visible light if we warm up materials at least several hundred degrees above our room temperature.
Electric current is a way to generate heat. That's because moving electrons contain extra energy. Besides it they are part of the electron cloud in the solid and obey its statistics so they emit photons and finally cause thumps to atoms. Due that energy loss the drifting motion of the electric current electrons in solids is very slow, only in vacuum electrons can get cosmic average speeds. But the number of drifting able electrons is especially in metals so high that substantial currents are possible.