lighttpd and ngingx

Correct, these are HTTP daemons that do the same job as Apache, but are generally geared to different kinds of content serving. I don't know much about them (I'm an Apache/IIS man myself), so I don't know why you would choose one over the other. I'm sure there's lots of questions on serverfault about why you would though.

For more information, try here or here or here or here or here.

FastCGI / CGI

CGI = Common Gateway Interface, and it was most commonly used to execute Perl and C scripts back in the 90's (or any pre-processor). Please correct me if I'm wrong about that. PHP also ships as a CGI module, and it's just an (old fashioned and slow) way of exposing the PHP engine to the HTTP daemon.

FastCGI = a modern implementation of CGI, which is apparently quite good. It's an alternative to ISAPI plugins for IIS and Apache modules.

Static Content

There is absolutally no reason to set up a 2nd server for serving static content. If you're serving images, it's usually a good practice to have a 2nd subdomain to serve your images from, as this means that useless information like Cookies are not sent with the IMG requests. The usefulness of this really depends on your expected traffic levels. You should be able to configure this in Plesk.

You can manually set the content type for specific file extensions in the web.config file for each web site where this is needed. In the root for the site, find the web.config file and add the remove and mimeMap lines as below (or create the entire file if it doesn't already exist).

<?xml version="1.0" encoding="UTF-8"?>
<configuration>
    <system.webServer>
        <staticContent>
            <remove fileExtension=".html" />
            <mimeMap fileExtension=".html" mimeType="text/html; charset=UTF-8" />
        </staticContent>
    </system.webServer>
</configuration>

Sample taken from a discussion on the IIS Forums which addressed this question.