Once you make the moon the intermediary for the sunlight, you now have to consider the moon as the source for the thermodynamic argument.
No, you don't. Otherwise light reflected from a mirror wouldn't be able to make an object hotter than the mirror, which is obviously wrong. Technically speaking the constraint is more than just the frequency of the light: for example, a laser has "negative" thermodynamic temperature, which means a laser beam can heat an object to an infinitely high temperature (theoretically), despite being, for e.g. an infrared laser (although since the object you're heating up tends to radiate energy as it's temperature to the fourth power, you quickly need a really, really powerful laser to get to high temperatures).
You can, and they do. Matter particle wavefunctions were proposed by De Broglie in 1924 and confirmed experimentally the year after. Interference between matter waves of whole atoms was demonstrated shortly after.
In our modern understanding of physics, every "particle" is a wave in a superposition of waves in a field.
The waves in quantum mechanics are probability waves. While it is true that those can create interference patterns, when they do so they only alter the probability of finding the particles in particular places. You can't add together two particles together in QM to create a new particle with twice the energy (not least because doing so for massive or charged particles like cosmic rays would violate the corresponding conservation laws).
Pure quantum mechanics per se doesn't even have creation or destruction operators for particles, you need relativistic quantum mechanics (i.e. quantum field theory) for that. In QFT, particles do become elevated to not only probability waves but to freely propagating disturbances of the underlying field (for e.g. the electron field for electrons, or neutrino field for neutrinos. Once you do that particles can interact with each other to create new particles, but the physics for that still don't allow "rogue wave"-like behavior, and again you still need to obey conservation laws, so two protons can't merge together to form a single proton because that would violate charge conservation (and they can't even collide to produce two protons, one with very high energy, because that would violate conservation of energy/momentum)
Byte your tongue.