The Malicious Software Removal Tool is often a part of windows security downloads and I always allow it to install, but I wonder, is this tool something that always installs itself directly? Or is it savable and is there a way to 'run' the tool anytime I want? In other words, is it available for manual use?

Unfortunality no. Here is Microsoft´s description

"The version of the tool delivered by Microsoft Update and Windows Update runs in the background and then reports if an infection is found. If you would like to run this tool more than once a month, use Windows Live OneCare safety scanner.

No you won't be able as "touch" mentioned before. It is an automative program(run on background).

You may use the software "touch" mentioned or even other spyware programs like Ad-aware, of Spybot etc...

Please tell me that is not the only protection you are using !!!