I had to research this myself as I didn't know: if you're running CGI, in phpinfo() output on under "Environment" you'll see a lot of variables, the most important one is "REDIRECT_HANDLER". If you're running fastCGI you'll most likely see only "PATH".
not sure what that thread was about... if you have access issues those will clearly be marked as such in Apache's error.log. Until you see 404 errors and evidence in error.log, I woundn't worry about that.
Those issues show up in error.log, I don't think such script would be very valuable. What you need to worry about are files and directories that are too open. For these, you can use find:
$ find . -perm -o=w
will show you all the files and directories that are writable to all (which is not always necessary).
FastCGI is usually the best choice for WordPress. CGI is only useful when your main use case involves uploading large files via PHP: in such cases, FastCGI may timeout while CGI processes may not.
You can run a http stress test tool to your site and check the response time. Run the test using both CGI and FastCGI configuration with a simple tool like autobench http://www.xenoclast.org/autobench/ ... Have a go at it and let us know what you find out.