Is there any possible way for alien life to be based on a dark matter biochemistry or at least be dependent on it in some way?
To clarify things: I am trying to base this on what is currently known about dark matter.
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Not made from the dark matter we have evidence for.
We've never observed dark matter directly, only indirectly. What we have seen is evidence that some kind of matter exists which does not interact with ordinary matter or with itself except by means of gravity. The stuff we've seen evidence of does not interact via the strong or weak interactions and -- most importantly -- neither does it interact by electromagnetism.
Given that, there does not seem to be any way for dark matter particles to attach themselves in clumps and build up atoms and chemistry. And without that, there appears to be no way to build the complex chemistry and structures of life.
We don't know a lot about dark matter yet -- and there is a significant, but respected minority of physicists who think that the evidence for dark matter is so weak that we shouldn't even say we have indirect knowledge. But whatever-it-is that we're observing, it's not at all like an invisible form of ordinary matter, and probably can't evolve life.
(After the edit:) That's the story about the real dark matter.
The dark matter you've invented has whatever properties you've given it and there's no way that we can say yea or nay to your question.
If your willing to take some liberties and accept theory as fact for your story (or what ever your using this for) you could have a weak force metabolizing WIMP based life-form. It is theorized that WIMPs make up dark matter and since they and the weak-force go hand and hand so well, it could be an opportunity for a very alien creature. And if you aren’t familiar with the weak force then it is basically what cause particle radiation. When the strong force isn’t strong enough to overpower it in the nucleus of an atom it breaks off the subatomic particles of atoms. The weak force is surprising similar to the electromagnetic force (which is what our metabolism uses) so it could work. So yes life based on dark matter could work, this is just an example.
All life needs to develop is a pattern that can replicate and the ability to do so imperfectly. Given those two features, life can eventually emerge in any system, from normal solid matter, to plasma, to whole universes, to idea-based life(aside: idea-based entities, aka mementic entities are WEIRD).
Dark Matter has been shown to exist in clumps in the universe meaning it can form patterns, and they're not perfect is symmetry, so they can be imperfect. So the answer is yes, the main questions are how likely it is, and what mechanisms under which might it function? Could it develop complex life, or are we talking something the size of a galaxy necessary to achieve the awareness of an Ameoba? Or something the size of an Ameoba wit the awareness of an entire city of people? Those questions we don't have answers to, as we don't know enough about extraterrestrial matter-based lifeforms, let alone know enough about how necessary properties would emerge in exotic matter types we don't understand yet.
That said, 'biochemistry' probably doesn't play into it, as chemistry as we know it relies on the matter we're familiar with.
But still, although we don't know the details, the answer is "Yes".