You might be right. I interpreted it as "when you measure a photon's wavelength, what is actually being measured?" Typically it is the energy of the photon that is being measured. Then the wavelength is calculated. I may have been too literal.

I mean, to OP it seems like they're mystery balls. I don't feel "self-propogating oscillations in the electromagnetic field" is very helpful as an explanation... you can critize what I've put down, but maybe try improving on it rather than just listing the definition and feeling superior.

As far as model 1 vs model 2. They're both kind of incorrect. A photon is not like a neutron. Photons are massless (not exactly because they have momentum, but that's the way it goes...) a photon is also not the "medium" through which EM radiation travels. A photon is a way to "quantize" (or break down into the smallest possible unit/packet/measurable piece) a beam of light.

Another way to view it: When light is emitted, it is quantized (discrete). It is not continuous. When you turn the dimmer switch on an LED, it doesn't produce a bigger or smaller light beam, it produces a larger or smaller number of photons. Each electron you pass through the LED excites an electron to later decay back to ground state. This decay emits a photon. The more electrons you pass through the LED, the more photons get produced, these photons constructively interfere to produce a higher intensity light.

Try not to think of a photon like a tiny ball of something. It is just a term to describe a unit of a type of energy.

A lot going on here. I think of a photon as a packet of light energy (frequently this is referred to as a "quantum" of light energy). This packet consists of some electromagnetic distortion. This distortion has a wavelength and a frequency. These values are interchangeable due to the speed of light. Additionally, through the speed of light relationship, the energy of the photon is defined by its wavelength and frequency. We can then measure a photon using a photodetector. Think of a photodetector like a solar panel with more precise electronics. When a photon hits the photodetector, it transfers its energy into a semiconductor, the photon energy is absorbed and converted to electrical energy. The electrical energy is measured and then we can work backwards from electrical energy to photon energy to wavelength.