Can I defrag my hard drive while downloading a file, if the file is on an external hdd?

"Yes, you can defrag your disk. If you're using IE, though, the file gets put in your temp folder until it's fully downloaded at which point it gets copied to its final destination so you may still be downloading to your hard drive and not to the external disk.

It's certainly a good idea, though, to leave your machine alone while defragging and really best if you can defrag the drive while it's not being used. The c:\ drive of a Windows machine that is in use is constantly being written to which lowers the effectiveness and extends the time required for a defrag. Best to boot to an alternate drive and defrag with no activity.

Edit:
I agree with nik about not using the building defragger, it's quite clunky and slow. Have a look at this question for other defrag software suggestions."

The defragmenting process is using a separate disk entirely so it shouldn't be affected. You could even download it to the disk that's being defragged if you really wanted to.