How do we know dark matter isn't just really transparent matter? Like, we can't see it in space but it's there, not reflecting or deflecting enough light for us to detect it.
Because it would collide with itself. Dark matter isn't just "not visible" - it's non-electromagnetic. As observed it didn't aggregate when colliding with itself, so there aren't big dark matter made black holes around, nor gravity anomalies from dark matter nebula or the like.
Two dark matter particles headed directly at each other would pass through each other and be only slightly deflected by their gravitational interaction.
Not necessarily. Dark matter could be made of small dense objects. Because they are small, we wouldn't see absorption of light. And because they are small, they will very seldom collide. These kinds of object are called MACHOs.
Based on observed dimming events while monitoring many stars, we have ruled out brown dwarfs as more than 20% of the total. Other possibilities still remain, but none have shown evidence of being sufficient to explain dark matter. However we have not ruled out the possibility of it being something that we haven't thought of yet.
It could be[0]. It's just not very likely, since you'd have to have very special circumstances, but it's not logically impossible, at least in cosmology.
From what I understand, if dark matter is stuff that only interacts gravitationally, by definition it is transparent to light. Also collisions, being ultimately electromagnetic interactions, aren't observed. So it's not transparent in the sense of glass. But I'm not a physicist, and this thread is interesting :)
