We know pretty well what matter is and how it interacts with the others.
Dark matter interacts through gravity but not light. Beyond that I haven’t heard much else.
And lastly anti-matter has an opposite charge and interacts with matter through annihilation. I think I remember hearing that it would react with dark matter the same way.
So my question is, does anti-dark matter exist, and what are it’s properties?
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.