Does dark matter interact with other dark matter, besides by gravity?

Supposedly dark matter is matter that interacts with normal matter by gravity, and little or not at all by any other force. But how does it interact with other dark matter? Also only by gravity, or could there be other forces that affect it?

If only gravity affects it, would it tend to collapse to form "dark black holes", and if so, would those be indistinguishable from normal black holes? I would assume they would be pretty similar, since in any case we can only detect black holes through their gravitation. Only perhaps dark matter black holes could occur in other mass ranges besides stellar mass and supermassive.

Or would not having other interactions besides gravity prevent accumulations of dark matter from being able to shed excess kinetic energy and angular momentum, so that they couldn't collapse, but instead would orbit the center of mass. Isn't it possible to still shed energy via tidal interactions?

Supposing it does interact, is it possible that it has an exactly parallel set of interactions to normal matter, so that there is for example a dark electric charge, where dark positive charges attract dark negative charges, but have no effect on normal matter positive and negative charges. And dark charges imply a dark photon to carry the force. Dark strong forces would allow dark fusion in dark stars. Doesn't that blow your mind? There could be a whole parallel galaxy to ours occupying the same space.

Is there anything that isn't possible about that hypothesis? How could we test it? With sensitive gravity probes could we start to map the dark matter in our nearby interstellar space to a high degree of accuracy?

If galaxies are filled with dark stars radiating dark light, could dark light be dark energy? Or is it still not enough to account for all the dark energy?