I have one external USB HDD and I use it for backup and hold personal data (off-line, non-connected to the Internet).
I think that you won’t be able, in most circunstances, to install programs in it. It’s like to install in a CD or floppy. The setup programs won’t allow.
If they allow, you won’t run your laptop faster just because of this. On contrary, the access to USB will be slower than to the laptop HDD.
Anyway, can you say how much free space you have in your laptop HDD? 8)