On multitasking:
iOS 4 is coming to iPad sometime in November, and it will bring the same multitasking functionality that the iPhone already has to the iPad. Right now, you can listen to music in almost any app (some will kill the iPod app in favour of their own audio), but you wouldn't be able to flip between a notes app and a pdf reader, as in your example. That said, there are quite a few apps which will let you annotate pdf files, and jumping between apps is often so fast that I don't miss having multiple open windows.
On writing with the iPad:
The on-screen keyboard is more capable than I thought it would be, once you learn a few tricks, but I wouldn't want to write a term paper on it. I use it to take notes in meetings, type up e-mails, and post on the internet, but for really serious writing, you need a really serious keyboard. You can use Apple's keyboard dock or a bluetooth keyboard for this, but at that point you lose a lot of the iPad's portability advantage. iPad should work fine for research, notes, and playing around with ideas, but once you're ready to sit down and type up a report, you might find yourself wanting a more conventional computer.
I've heard of some people who use the iPad like a second display while writing. They prop it up next to a desktop and use it to pereuse a web page or pdf while typing up text on their main machine. I'm not much of one for dual screens, so I can't personally vouch for how effective this is.