Dark matter interacts via gravity but not electromagnetism (including light). So its particles would have no electric charge, and thus no distinct antiparticles.

There are hypothesis that dark matter particles are their own anti particle, which would mean that they would annihilate when they come in contact with each other.

The people looking for them are examining high energy bursts around supermassive black holes as potentially coming from that. No idea how they could ever approach finding any evidence for that. But that's their problem.

I think I remember hearing that it would react with dark matter the same way.

Like matter, it doesn't interact with dark matter to any detectable degree.

I say "doesn't" on purpose, because we have small containers of the stuff tucked away in labs, and it's (momentarily) created as an inevitable byproduct of particle accelerators and certain radioactive decays.

So my question is, does anti-dark matter exist, and what are it’s properties?

Nobody knows what dark matter is beyond it being everywhere and heavy, so double don't-know. There's no particular reason to think it would follow a similar pattern, though.

The problem with dark matter is that we don't know what it is. If it's a particle, then presumably there probably would be an antiparticle for it. However, we don't actually know if it's a particle or not.

There's some hypotheses that say that dark matter doesn't physically exist, and that our theories of gravity are just incomplete. There's some other hypotheses that say that dark matter might be really small black holes. And then there's some hypotheses that say that dark matter is a particle. Until we find out more about what it is, we simply can't say for sure what sorts of properties it has

Antimatter interacts with regular matter in more ways than just annihilation. Annihilation just happens to be a process that’s uniquely available to antiparticles and has a high probability of occurring. This is because antiparticles have both opposite electric charges to standard particles and opposite color charge, so annihilation between particle/anti particle pairs conserves these quantities.

It’s unlikely that there’s an anti-matter equivalent of dark matter. If there was, we’d expect to see annihilation radiation, such as the 511 keV photons emitted when positron+electron pairs annihilate.

What are "the others"? Non-matter? Anti-matter? Non-Dark Matter? Matter is well defined by Einstein's equivalence principle: E=Mc^2, but what are "the others" it is interacting with?

"Dark matter interacts through gravity but not light"? What is implied here?? I would argue that more accurately, dark matter is observable through gravitational anomalies, which has nothing to do with interacting with anything, including gravity or light.

Just because it is called "dark matter" doesn't necessarily imply that it has anything at all to do with "matter". Presuming that the term "dark matter" would be analogous to "matter" in some theoretical way, and therefore must exist in our universe in a corresponding "anti-dark matter" theoretical way, would be removed from the process of scientific exploration or critical thinking, since that is not how dark matter has been observed in our universe.

The descriptive words humans have devised to describe our reality are just that, human derived. Matter, anti-matter, and dark matter exist regardless of whatever names humans have assigned to them. Just because 'anti-matter' exists in our scientific lexicon (having observable traits) as a word implying the 'opposite properties of matter' means nothing about the observable properties of 'anti-dark matter' whether it exists or not. The fact that we do not even have any ability, scientifically, to observe the actual properties of dark matter within our scientific understanding of reality at this time implies that no, 'anti-dark matter' doesn't exists, presumably only until someone observes or predicts it. Arguing that 'anti-dark matter' exists on the basis that 'anti-matter' exists simply ignores the scientific method.

To my understanding, dark matter and dark energy is just a placeholder name for things we can see evidence of via influence on other things, but we don't actually know what they are exactly. It could be a multitude of things, not just one.