That's exactly what neutrinos are in terms of human experience. Ridiculous amounts of neutrinos are flowing trough the whole planet and trough you like we are nothing.
In realm of everyday experience neutrinos and proposed dark matter would be the same ghostly thing.
No, but as a posteriori reasons go "everything else couples to the weak force" is a pretty good one.
> them dark matter is unfalsifiable
Only insofar as all the ontological content of a physical theory are unfalsifiable: you can always shift complexity around between state and dynamics if you're willing to pay the price in elegance. Consider Kaluza-Klein theory, for instance. In some sense this demonstrates that classical electromagnetism is unfalsifiable - but no one actually cares.