Some advice please
 

Cutting straight to the chase:
I've got a Toshiba M1 laptop but I can't change anything on it since it's not mine.
I want to run Linux on it so I use Knoppix.
What are the pro's and con's of an external hard drive - will I be able to boot from it and how much slower/faster than Knoppix will it likely run (based on the data transfer limits of USB, firewire etc)

This is really difficult to answer numerically. You should expect some performance gain but I cannot say how much as I have never done such a thing.

If you have the external drive at hand then you should give it a shot. I don't know if I would invest in one if I didn't have it though. Except that it provides a good way to save your working files.