How does FastCGI affect Joomla?
When PHP runs from FastCGI, your server runs the PHP interpreter like an Apache module, but with the rights of your user account. Usually, the PHP interpreter is either running as the user of the webserver (which is fast, but insecure, since everyone's scripts run with the same rights), or as a CGI program, which is slow. Thus, FastCGI is a good solution for shared hosting.
Since the PHP interpreter runs as a single instance, it does (AFAIK) not parse the .htaccess or php.ini files per directory. To change php.ini settings, your host must offer you a method to set up or modify your own php.ini, or at least parts of it. Here is how one of host does this: it parses one php.ini file (which the user can modify) once an hour, and puts some well-defined settings into the web server's main php.ini file. Thus, users are able to change some settings for their site only, such as turning register_globals off, switching between PHP4 and PHP5.
If your server uses FastCGI, you can ask them to enable a method such as the above example, or you may be able to ask them adjust some settings for you.