Can I set up a BCM database on SQL 2005 64-bit edition?

Database Tool is not supported on 64-bit SQL 2005.  However you can try a manual workaround by following the instructions in the document given bleow.

http://sharepoint.microsoft.com/innovateon/officedeveloper/Developer%20Documents/Outlook2007BusinessContactManager.doc

After deploying the database, how do I add and remove users?

The BCM database sharing wizard handles adding and removing users.

On the client side, BCM installs SQL Express even if you have no
 intention of using it. Is it necessary?  

It's not necessary to have sql installed on a client that will only
ever connect to a shared database on a server, but it is recommended to have it installed.

On our SBS server, I would like to change the location of the BCM database
files (MDF, LDF, BAK) to something other than the default "Application Data"
folder in "Documents and Settings".

Download SQL Management Studio from Microsoft Website (if it's not already on your SBS
server)Open SQL Management Studio, expand the Databases section in the left navigation   bar, right click on your database, choose Tasks > Detach.  To ReAttach, right click on Databases and choose Attach, then browse to the location of  the MDF file on your hard drive..

Need to setup Accounting 2008 Pro and Office 2007 Pro linked to
Business Contact Manager on Small Business Server.

Database Admin tool can help you setup database on your SBS server. Also you do not need Office installed on the SBS server.