We observe patterns of behavior -- orbits, movement, gravitational lensing -- that are exactly what we would see if, for example, there were great clouds of matter or other galaxies in those places. But we don't see the hydrogen gas. We see non-uniform distributions of dark matter mass that imply there is not simply some consistent calculation error, but rather that there is dark matter that is not uniformly distributed. Again, read up on the Bullet Cluster because it shows a VERY clear example of what I am talking about, where the regular, electromagnetically-interacting matter behaves one way but the apparent shadow of dark matter behaves in a different way that is consistent with lack of electromagnetic interactions.

We've also discovered things like ultradiffiuse galaxies -- likely remnants from ancient collisions -- that have apparently been stripped of their dark matter. MOND cannot explain these observations because these galaxies essentially behave in a Newtonian manner that would be impossible in a MOND framework.

if it has mass, why does it not just clump together?

Why does stuff clump together? For all non-dark matter, the answer is electromagnetism. Outside of the extreme cases of neutron stars and black holes, where gravity overwhelms and defeats electromagnetism and the nuclear forces theoretically take over to create degeneracy pressure, electromagnetism is the reason things clump. Absent electromagnetism, what would cause clumping? Essentially nothing, stuff would whizz straight through other stuff and go into orbits. Potentially HUGE orbits, which is why there's so many theories around dark matter "halos". Maybe if there were DIRECT collisions of theoretical DM particles, that might cause an energy-releasing event -- this is one of the things current dark matter detectors are looking for and may yet find within the upcoming years.

are there any theoretical works on what kind of particle this could be, matching the pattern?

Yep, and more than a handful Many that make specific predictions we can test for and so are testing for. For example, you could look at axions, which are a theoretical particle predicted by an entirely different theory that may be a good fit for the dark matter particle.