You are aware that you might be able to run Joomla on a windows based server, right? From the Joomla! 1.5 "System Requirements":
"Joomla! is developed and tested primarily on the Apache web server versions 1.3.x + and 2.x +. Whilst there is every chance that it will work with other systems, such as Windows IIS, these are not necessarily supported as fully/at all within the technical support community... Joomla! has been successfully tested on many variants within the main three OS for Windows, Linux, Apple Mac OSX. It may well work on other platforms but this is less well documented."
Sure! You can stick the whole Joomla site behind apache authentication (.htaccess based password protection).
As an alternative approach, you can also leave the site itself "open to the public", but have any and/or all the content restricted from view by other than authorized users by the Joomla system itself!
I don't understand this question at all ... All you need to access a Joomla! based intranet is a browser. To connect from the school, you would need to be able to browse to the Joomla! site, but that is about all. Being able to SSH and/or SFTP to it would be nice, but is not absolutely necessary.