Is it possible to run two websites with different domain names on the same apache server? If so does anyone know how?

Absolutely. You can have many virtual hosts. Check the bottom of the httpd.conf or your reference for more information. These virtual hosts can be configured to listen on different IP's. But that isn't required.

What SilentRage said. This is a very easy thing to do under Apache. However, if you plan on running more then one or two, I'd suggest creating a seperate file to manage them. Then adding in an Include directive to include them into the httpd file. An organization issue. I always do this as my server has many different names that it has to pretend it is.

I'm also thinking of writing a tutorial on Apache. Is there anything that anyone would like me to cover in said tutorial? If I have enough interest, I'll write something fairly detailed and oriented to the people who are interested in it.

Yeah, if you could include integrating Tomcat and Apache together, that would be great.