A neutrino condensate would involve lowering the energy of a pair of neutrinos. The only particles that could participate in such interactions would be those that are already at the top of a degenerate "Fermi sea" of neutrinos. In other words the formation of pairs would have the effect of "squaring off" the occupation index distribution and leaving a small gap between the top of the Fermi sea and a small number of higher energy neutrinos; in much the same way that pair-forming in neutron stars only acts on the small fraction of neutrons with the highest energies.
As such, there would be almost no effect on the bulk dynamics of the neutrino fluid and the Tremaine-Gunn (1979) restriction on forming galaxy halos from light leptons would still be a problem. The bulk of the neutrino fluid would still be degenerate and it would be impossible to pack enough light neutrinos into the available phase space.
Aside from this - what is the long-range pair-forming interaction that can work between particles that only interact via the short-range weak force. Gravity? Two neutrinos separated by $10^{-5}$ m (from the number density of ~0.1 eV neutrinos needed to explain galaxy halos) have a gravitational potential energy of $\sim 10^{-23}$ eV. So they would have to be colder than $10^{-19}$ K to avoid the pairs being thermally broken.
If the neutrinos are just meant to contribute to some general background rather than to galaxy halos then the question arises - why wouldn't they concentrate in galaxy halos in the same way? In any case the universal average density of dark matter would suggest a neutrino number density (assuming the same rest mass) about 3-4 orders of magnitude lower than the concentrations in galactic halos. This changes the average separation to $10^{-4}$ m and thus the pairs would have to be colder than $10^{-18}$ K.
I don't see the merit of this hypothesis if the proposed dark matter doesn't actually explain most of the problems that dark matter is required for - i.e. galaxy and cluster dynamics and point #5 is incorrect (as well as #7 that was originally part of the question I answered).