[semi-extrinsic]

As for 2: YMMV, I always took good notes and aced all my undergrad (and most of my graduate) math. I've seen several studies showing that retention of material covered in a lecture is significantly better if you take notes.

I think the key problem for most people is speed: if you need to spend so much effort just on the note taking that your brain can't process/understand what you're writing, then obviously taking notes is a bad idea. I don't think this is accounted for in the aforementioned studies.

[Davidp00]

Do you have a link to that study?

I remember seeing a study that showed that people who take notes on paper do better vs people who take notes on a laptop. People who didn't take notes(or take very few) weren't mentioned.

[semi-extrinsic]

You're correct that most new studies compare handwritten vs. laptop notes. The effect of handwritten notes vs. no notes was studied quite a bit earlier, and I believe this effect is now as uncontroversial as psychology can be.

A good review of the literature (from 1989) is found here:

http://link.springer.com/article/10.1007%2FBF01326640