A) On installation, Zope installs Zserver. Is Zserver better than Apache?
No. It is different. I personally host just out of Zserver because it is easier to set up, a bit faster and easier to move. I can tar up my installation drop it on another box and restart ZServer, no fuss or muss with Apache.
Does it run better with Zope? Can I do the Virtual Hosting with Zserver?
Apache can do a lot of things through loadable "mods" that ZServer cannot. If you are just going to be using a 100% full Zope installation with all of the content stored in Zope you might as well just use ZServer.
B) We are currently using MySQL. Does Zope plug-in to MySQL by default, or does it use it's on DB?
ZODB is its own "object database" not a relational database like MySQL. There are connectors to allow you to talk from Zope to MySQL.
We have 6453 files on our IntrAnet and 3003 files on our Public page. Is this exceeding the boundaries of Zserver's capabilities?
Not at all. It is a large amount of files so your Zope Database (see above) will be large. Make sure to put it on a machine with a good amount of RAM (Zope loves Ram). Cheers, BZ