We have many theories that advocate the particle nature of light. But have we ever observed photons physically?
If so: what do they look like? How big are they?
If not: why not? Is it because they move at the speed of light?
Electromagnetic Radiation – Appearance of Photons Explained
electromagnetic-radiationphotonsvisible-light
Related Solutions
Your assumption that pair production is ruled out, rules out* that two photons interact through higher-order processes. Quantum electrodynamics tells us that two photons cannot couple directly. That leaves us with classical electromagnetism, which tells us that electromagnetic waves pass through each other without any interference.
*Edit. The photons can interact through higher-order processes. As pointed out in the comments (and I hope I'm getting this right), there is a (quite small) probability amplitude for two photons to get absorbed in, and two photons be emitted by, e.g. an fermion-antifermion virtual pair (which is the leading contributor to the combined amplitude of all such processes). Whether (and this is my cop-out) the emitted photons can be considered the same photons as the absorbed photons, I leave to the, certainly more knowledgeable, commentators.
The first 2-D image you posted is a typical simplification for teaching purposes. In it, they use the height of the sine wave to represent magnitude, and the directions of the sine waves to show how the fields point relative to each other. The light itself however is not itself at all cone-like. You have to imagine this sine wave existing at multiple points in space, not localized in this cone-like volume. This can be difficult to visualize.
A common method for visualizing these kinds of fields is a 3-D vector field plot.
Length or colour will typically correspond to amplitude, and the arrows show direction of the electric field. The magnetic field is always perpendicular, and the amplitude is proportional, so there's little sense in plotting both together. This one I've included shows how the field actually permeates a volume.
Out of interest, here's a gif of dipole radiation. This is just a 2-D slice of the field, and doesn't show vector direction, but is a very good visualization of a more real-life kind of radiation. Colour corresponds to magnitude in this case.
Best Answer
Do we see an electron?
We see the path of an electron in a bubble chamber, the track it leaves ionizing the atoms.
At an individual photon level, we see the footprints of photons, on a sensitive surface where it scatters and leaves a dot.
Elementary particles cannot be seen in the way we see objects, only their interactions. The photon is an elementary particle.
Note: the link I had for the photons is not working correctly, there seems to be a reorganization and this particular article cannot be found. I will be checking. This paper has the original experiment. This is the correct link for the "wave particle duality for the classroom".