I'm only very casually knowledgeable in QM, but my understanding is that photons are waves that propagate through the electromagnetic field. They are not the medium, the medium is the field.

As for measuring their wavelength, the most classic example is using a double slit to create a wave interference pattern, then measuring that. Lasers make this easiest and most accurate but it's possible to get an idea of the scale of these wavelengths even using white light.

Lastly, wave particle duality and the uncertainty principle don't really work with most "mechanical" interpretations, at least in a general sense. They're helpful if you're thinking about specific aspects of photons and other particles, but the reality is that quantum behavior just has different rules and trying to understand through the lens of more intuitive mechanics just doesn't work all that well a lot of the time.