I'll give you my take on your questions, as someone who works often with the
photon concept:

To the extent that any particle "exists", yes, photons do also. I would not say they "are" energy, I would say that "have" energy. What they "are" is photons, that's it. Energy is just a property that has proven useful to define in the manner that it is defined, and in different situations what we mean by energy is actually a bit different. It is a common misunderstanding that energy is a "thing" of some kind, rather than an attribute.

They could be anything, of course, but our understanding of them that works very well is that they have no mass, in the sense of rest mass. They do not need to have mass to be a particle, as mass, like energy, is simply an attribute, not a thing in and of itself.

Spin is a very weird and profound attribute of a particle that controls a lot of things. It controls the angular momentum of the particle, from the point of view of angular momentum conservation, and it also controls whether or not you can have more than one identical particle in the exact same state. You can just think of it as internal degrees of freedom that says two otherwise identical particles can be in different states even if they are moving in exactly the same way. Photons have spin 1, which means you can put as many identical photons into the same state as you want, and it also connects to the fact that the classical description of how photons move can have two distinct polarization states (like polarized sunglasses only letting in light that is vertically polarized, not horizontally).

What is meant by "decay" is spontaneous decay, in other words, photons don't just suddently pop into something else for no apparent reason. However, they can be destroyed, not just converted into a different wavelength. Photons from very early in the Big Bang were destroyed, and replaced by lower energy photons, which were clearly different photons, and which have since been redshifted to even lower energy by the expanding universe.

Since photons carry energy, to stop or destroy a photon you need to have some process that can accomodate that energy. The higher the energy the photon, the fewer the processes that foot the bill, and so the less likely the photon will interact. Even if you are talking about scattering the photon rather than destroying it, there is still a dependence on the energy of the photon. An analogy might be firing bullets through a wall-- low energy bullets might have to hit a window to get through, high energy will just plow through.

No, not very likely. There is always some probability of almost anything happening, but when the probability is so low that it's pointless to even contemplate, we say it doesn't happen. Infrared photons emitted by the Earth must all come from very close to the surface, or they would have been re-absorbed and turned, at least temporarily, back into heat.

Yes, photons with the same attributes are indistinguishable, but it's not just wavelength, spin (polarization) is also an attribute.

A photon is a quantum mechanical particle, and as such, it has no definable trajectory. However, in many applications you can treat it as though it did have a trajectory and get the right answer. If you are doing that, then the photon trajectory can be altered by scattering. However, in astronomy we typically observe the photons that have not been scattered on the way. In cases where the wave property of photons is important, such as for radio waves, the concept of trajectory breaks down and the waves are affected by the medium through which they pass even if there is no obvious "scattering".

You are referring to the wave function, that is the only sense to which photons travel like waves. Classically, we can measure an electromagnetic field which is also a wave, but this is due to many photons and is not the particle picture.

Not sure what you're getting at here, but it doesn't sound like a picture you'd want to adopt.

It's an attribute, with various properties that involve conservation of energy and other things. It is not a thing in and of itself. The sci fi idea that there is such a thing as "pure energy" is bogus, you may as well say "pure telephone number".

Yes, but distant stars don't contribute much to the photon density from the Sun in the daytime.

Don't forget neutrinos-- there are a lot of those too.

I don't recall saying that, but low energy photons such as we experience every day do not interact with each other, and they can occupy the same space (a property of their integer spin). Very high energy photons will scatter off each other because they can make particles and antiparticles which may then annihilate. I don't know if very high intensities of low-energy photons can find ways to interact or not, but it's very unlikely.

Yes, photons don't "contact" things. Their wave function is affected by the thing, such that you can get a reflection, like from a mirror. This has to do with the rules of waves, and how they interfere constructively or destructively, just like sound waves bouncing off a wall.

There is no principle of conservation of volume, and energy can be converted into mass, so yes, photons can be converted into matter. The key is not to have a lot of them, it's to have high enough energy in each photon, to be able to convert it into a particle of matter (generally electron/positron pairs). In that case, one photon goes into one electron, they don't aggregate (it's very unlikely).

That is a pretty good question even for trained physicists. All I can say is, energy is as energy does, don't try to think of it as a thing in and of itself. It is a property that obeys various rules, it is a useful construct. It may not be anything "real", in the sense that aliens who do physics might not use that concept at all. It's pretty darn useful though, so it's hard to imagine physics without it.