As other replies have said, neutrinos move too fast. They seem to move almost exclusively at the speed of light. (So close that we can only infer indirectly that they don't ... and it's possible that one kind still might.)

Unless the galaxy were a black hole, they'd escape. Since it's not, it can't be them.

It would be great if there were something producing slow-moving neutrinos, which would not only solve this but give us a huge leg up in understanding what's going on with neutrinos. But it doesn't look like that's the case.

Pretty sure. The problem is, that neutrinos are too light, and when they are produced in the early universe they are too fast. That means galaxies do not form like we observe them. Basically, neutrino dark matter would "orbit the outskirts" of the galaxy instead of building a defined center.

As others have said, they are too fast. But that just raises the question of why do we expect that if dark matter is particles they must be slow?

The episode "Is Dark Matter Made of Particles?" [1] of PBS Space Time covers that.

They have several other dark matter episodes looking into other possibilities, such as black holes, axions, gravity not working the way we think it does, and more. If you are interested in this topic doing a search for "dark matter" in the video list on the YouTube channel would be a great place to start.

[1] https://www.youtube.com/watch?v=fidzLZQyaJE

Yes. We have a pretty good understanding of how neutrinos are created and destroyed and there should not be enough of them to explain the anomalous gravitation.

Everything we know about neutrinos says they move too fast to account for what we see. Doesn't mean that there couldn't be some discovery they completely changes our understanding of neutrinos though.