Is there a BeOS version of Apache (or WebSTAR)?
Apache is available. A number of companies are working on various Internet tools for the BeOS, including ftp and web servers. BeOS is not meant as a server OS, especially with excellent server OSs out there with more security and more server-oriented features, but people have served many sites from BeOS with no trouble, such as the popular http://www.betips.net.
In the meantime you might want to check out the port of Apache to the BeOS, Robin Hood (a GPL webserver from the amazing Joe Kloss) Zorro from LittleBig Software Engineering or diner from stegemann & stegemann.
Read more about the Apache port here:
http://dialspace.dial.pipex.com/town/parade/abb37/apache_beos.html
Find Robin Hood here:
http://www-classic.be.com/beware/Network/Robin%20Hood.html
You can read more about Diner on the stegemann & stegemann web site:
http://www.stegemann.net/Incorporated/Products/Diner.html
You can read more about Zorro on the LittleBig web site:
http://littlebig.rsn.hk-r.se/