About feeding answers--personally, when I am on, I am unable to so much as look at my laptop, much less a chat window on it, so any answer-feeding becomes largely useless. But perhaps I am just less skilled. I usually close everything but notes if I get called on so i don't get distracted. So don't look so glum, nu2bu
As far as note-taking, I actually don't think I type much faster than I write, given that I never really learned to touch-type, but I still prefer the laptop.
1) Making outlines is far easier, for the reasons already mentioned.
2) I would be pretty terrified of having only one copy of my class notes. You can't really back up paper notes, unless you want to photocopy everything. Given how important note-taking is (if it helps you that is) I think the ability to backup notes to a CD is invaluable.
3) If you want to take your test on a laptop, as you will be able to, well, you'll want it.
I would say at least 3/4 of my section used a laptop to take notes. Or at least had a laptop during class
Chaoslace7 is right about being disciplined and avoiding distraction (good luck!)
One more thing: If you already have a good desktop computer, or you don't but you really think the only thing you want a laptop for is note-taking, I highly recommend a secondhand or refurbished Thinkpad from IBM. They are super sturdy and really hold up well. I got an old THinkpd 250 off of Ebay for about 300 bucks, and it has a tiny drive and only 64 megs of ram, but 1) you can add more memory and 2) if it meets the minimum requirements for WIndows XP and you throw XP on there, it will run just fine.