I downloaded it, and extracted it into C:/perl/lib/Win32-IE-Mechanize-0.009

It doesn't really matter, but it's better to extract to some directory that's outside your perl tree - say C:/my_build/Win32-IE-Mechanize-0.009 for example.

Math::BigInt: couldn't load specified math lib(s), fallback to Math::BigInt::FastCalc at C:/Perl/lib/Win32API/File.pm line 20

That's merely a warning - it's harmless and you can safely ignore it. It comes from a bug in that particular version of Win32API::File, and that particular version of Win32API::File was included by mistake in build 1003 of ActivePerl. Afaik, other builds of ActivePerl are unaffected, as also will be future builds.

For mine, the only worry about what you have done is the failing tests - perhaps they're just the result of your firewall. (If you now run the test scripts individually as normal perl scripts, you'll probably get some verbose error messages that tell you precisely what is failing.) Other than that, just start using the module and see how it goes.

Cheers,
Rob