The self-interaction of dark matter may be small but it cannot be negligible if it is able to dissipate energy to relax into galactic clumps (necessary to explain galaxy rotation curves).
According to some answers in this old question: How Does Dark Matter Form Lumps?, the gravitational self-interaction alone is enough to allow dark matter clumping (via n-body interactions). Although two answers suggest something other than gravity is needed (one states considering the weak force is necessary, while another answer argues for why gravity alone doesn't explain how in cosmology dark matter could clump first).
I am curious about:
Have the measurements of dark matter profiles of galaxies become good enough to provide indirect measurements of dark matter self-interactions?
Can this self-interaction be used to say anything about the mass of the dark matter particles? At the very least, can we say with certainty they have mass above some threshold (ruling out very light particles such as axions or neutrinos, and ruling out some kind of unseen massless particles)?
Since the strength and radial distribution of the gravitational force vs the weak force differ so strongly, is it possible to determine from the self interaction whether dark matter interacts via the weak force?