Slow S/W...Run Parallels From External HD AND Locally?

Apologies in advance for a long and convoluted query, but I've searched the forum and haven't seen someone ask this...maybe because it is obvious to you guys (I hope not). Also - apologies for my lack of technical knowledge.

I have a mac (details below) and am starting a part time job where I'll need to run a windows based software that "reaches out" to a remote Windows Server, through VPN.

I have a very limited understanding on how Parallels works, but was able to install a trial on my Mac, then install Windows, then this software. And it worked! Lovely. When using the software, the Mac seemed to take forever...and even froze once. My friend suggested installing Parallels on an external HD (2 Tb).

A tiny bit more info: all data I'll be using with this software is stored on the server (not on my laptop). ALSO, I'd prefer to not always carry my external HD with me. Now the questions:

(a) Is it worth trying to install on my external hard drive and would the speed be noticeable?

(b) Is it possible to Install on both my external hard drive AND on my laptop?
If so, would I need to install (1) Parallels, (2) Windows, (3) Company Software on both...or would only Parallels be on both? Or (1) and (2) on both but (3) just on the local?

(c) Last question - if the software will be much faster, then I would be willing to bring the External HD with me everywhere. How would that installation go? Parallels on the external, Windows on the external, Company S/W on the local?

THANKS!!!!!!!!!!!
Colin


My computer's info:
Leopard 10.5.8
HD Size: 160 GB
Available: 18 GB
Model Name: MacBook
Model Identifier: MacBook5,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2 GHz
Number Of Processors: 1
Total Number Of Cores: 2
L2 Cache: 3 MB
Memory: 2 GB
Bus Speed: 1.07 GHz
Boot ROM Version: MB51.007D.B03
SMC Version (system): 1.32f8