First off, it is not likely that the hard drive speed is causing your slowdown so I do not suspect this will help that issue at all, but anyway ...
Yes, you can install Office to any HD you wish. First uninstall the existing copy and then reinstall using the custom option and you can specify a different folder/path for the install including putting it on the E: drive. This puts the actual application on e: but your data will still default to My Documents which, unless you move it, is on the C: drive.
Most people don't install the application on a different drive, what they do is put their data on the other drive. To do this you would instead install as normal but you MOVE your My Documents Library to E:
Your student keys are valid for an install to any harddrive (but legally limited to one at a time) so when you reinstall you will need to supply the license keys again. You should have them written down but if not, then before you do any uninstalling and reinstalling, you should install a freeware product called
SIW and go to the software - licenses section and get the keys (& this time write them down). SIW is listed in our
Freeware DB.
As I said, I do not think installing the application on a different hard drive will help with the slowdown issue. Moving your data to a separate hard drive might help a little. But the truth is it is the size of the files, the speed of your processor, and often, the amount of RAM (I recommend 4GB or better) are your most likely speed limiters.