If you can, try disconnecting the dvd drive from the laptop. Then boot up the laptop and see if it still goes slow. Either way it sounds like you'll need to replace the dvd drive. And when you got the msg about your hard drive, was it from within windows or during boot up before windows starts?
1)
www.tigerdirect.com usually has cheap stuff. Never bought a laptop hdd from them though.
2) Most software and drivers these days comes on cd so the external should work fine. If it comes on floppy you can burn it to a disk from you desktop.
Not sure exactly what you mean by semi downshifting, but working hard drive usually make a faint grinding sound.