Photons are a byproduct of electromagnetic waves. Due to the particular ways of which magnetic and electric fields interact, they tend to... produce the other. Specifically, a moving magnetic field produces an electric field, and a moving electric field produces a magnetic field. When these fields propagate through space, the magnetic fields are always perpendicular to the electric fields. Those electromagnetic waves that are produced from chaining electric field to magnetic field to electric field and so on. They also behave as the particles known as photons. Even electrons express this wave-particle duality. As for whether they can be created and/or destroyed, quite easily. When an electron orbiting an atom returns from an excited state (moved up an orbital), it usually produces a gamma ray. This gamma ray is a photon. As for whether black holes are slowly sucking up all of the photons... it is a bit more complicated than that. You see, photons can only move in straight lines. Gravity, however, bends the space of which the photons move within so that they appear to be traveling in a curved line in any particular inertial reference frame. Black holes possess an immense gravitational field, hence why they "suck in" photons- any that pass the event horizon will be trapped in such a way that no matter its direction, it will continuously be pulled closer to the singularity of the black hole.
As for how photons come about in nature, they are the process of which the electric force interacts. When two charged particles (two electrons, for instance) approach, they release a photon between the two that repels them from each other. An electron and a photon, by contrast, produce a photon in such a way that pulls them together. It is only through the interaction of the weak nuclear force between neutrons and electrons that repel them away so that they are not sucked in (as for the particle that mediates that interaction, they are W+, W-, and Z bosons).
When an electron moves from a state of higher energy to one of lower energy it emits a photon. They are, basically speaking, one way we perceive energy leaving a system. Another example of how energy leaves a system is as heat.
Are black holes slowly sucking up all the photons?
Not all, probably not even most. Just some.
Can they be created, and/or destroyed?
Yes, they are created as I, and for a more quantum take on the subject Ispil, have mentioned above. They aren't really "destroyed" so to speak since they are energy. They are absorbed by what ever they come in contact with and that energy is either reflected, stored or transformed into work or heat. Remember they are force carriers, so they are not really like other matter.
Besides, Hawking radiation (a credited model) which has yet to be proved does hyptoheises that as energy is sucked into an Blackhole, they would be also re-emitted back in radiation therefore the energy is simply returned back but with entropy being increased.
That being said, they can be created by 2 magnets as well, but they are not the usual particles but Virtual Photons but thats an simple idea. So every-time a electromagnetic being used the interaction is done by virtual photons. They can created in explosions, high energy particle collisions
are there infinitely many photons traveling past the furthest matter in the universe, forever?
Photons only appear when there is an interaction. An electromagnetic wave traveling through space is not a photon, but something different. You can sum up what this thing is mathematically with a wave function and give probabilities of it being here or there in some place and time, but what it actually really is, is unknown and perhaps beyond human understanding.
So, no, there are not infinitely many photons traveling forever, but rather a field of values that is constantly changing that has some value in all places and photons are not really real.
If that doesn't make sense, you probably understood it.
Also, there is a plasma "wall" a long ways out in the universe that prevents us from viewing that far out, for photons cannot bypass it. Source: http://en.wikipedia.org/wiki/Recombination_(cosmology) So no, there is not an infinite amount of light passing by an infinite amount of matter. It gets very, very complicated from there- the further past that "plasma wall" you get, the stranger things become. Think of it this way- at one point, the electromagnetic force and weak nuclear force were the same (electroweak theory) and the actual state of the universe was that of a very thick cloud of plasma. The cloud is so thick that no photons could actually travel very far; hence, no light truly "exists" past that point.
And Mats, there is the wonderful world of cosmic microwave radiation that fills most of the universe. They are technically photons, though this is just due to the fact that the "waves" that you mentioned are photons (wave-particle duality). Of course, there are other "things" that are in the universe that cannot easily be explained, such as the matter that is currently causing spinning galaxies to act as a unified whole instead of a giant spinning cloud (dark matter). Then there's dark energy, gravity waves, and the slew of mesons, bosons, hedrons, and leptons that float about... and don't forget those mysterious "ghost particles" that pop up in space in the absence of any other particles that prevent any possible "perfect vacuum."
And Mats, there is the wonderful world of cosmic microwave radiation that fills most of the universe. They are technically photons
Only during an interaction. It is not proper to think of them as being photons or of the wave traveling from point A to our telescope at point B. Experiments have shown that to consider light like this leads to incorrect conclusions. They are not consisting of a wave-particle duality - This seems to be something that is said just to avoid confusing the hell out of people - They are something totally different (and unknown).
Of course, there are other "things" that are in the universe that cannot easily be explained, such as...(dark matter).
Actually, dark matter is believed to be well understood. There is absolutely no reason to think that nothing (in terms of a particle with mass) lies between the current heaviest discovered particle (top quark I guess) and the smallest possible black hole, which is a massive void of potential energies for particles to have. In fact, super-symmetry models require them. There is some hope the LHC in 2015 might even observe some dark matter.
Then there's dark energy
Yeah dark energy is a real problem. Relativity predicts it just because the maths says you should add that term in (then it turns out to be there in the real universe). Quantum mechanics predicts it, but at a much much higher value than observed. Yeah we know it's there and it appears in mathematical descriptions of the universe, but our values are way out and it's a huge huge problem.
and don't forget those mysterious "ghost particles" that pop up in space in the absence of any other particles that prevent any possible "perfect vacuum."
This is not a surprise. Space-time cannot sit at a constant zero value (violation of uncertainty principle), so some quantum fluctuations are necessary.
Am I misunderstanding the seemingly clear message, or is the video just wrong?
Videos like this do not give a rigorous quantum mechanical description of the world. The modern way of looking at a photon is to say it exists only during observation and during all other times, light is not traveling like a bullet, it's not traveling like a wave and it's not traveling like some kind of duel particle-wave (to assume any of this gives incorrect answers). It is something completely different. The picture he paints of photons streaming away from the sun and us is good for the viewer, but not strictly correct.
Also, all attempts at grand unified theories I have seen make the photon lose its status as a fundamental unit, so for now the standard model views photons as indivisible (no misunderstanding on that part) and this seems like a correct view for now, but (when our theories and experiments become more precise) it may be proven otherwise.