Contacts are stored in your personal store (.pst) along with your calendar, inbox, outbox, etc. In order to have contacts show up as an e-mail address book, you need to check the following:
Right-click on the Contacts folder and choose Properties
In the Properties dialog box, select the "Outlook Address Book" tab
Make sure there is a check in "Show this folder as and e-mail Address Book"
The second part of your question is a bit more complex. You can't change the location of your personal store, per se. But you can add a new personal store service and delete your old one. So, if you really want to change where your pst is located, first copy your .pst to the new location. Then do the following:
Choose Tools - Services from the Outlook menu bar
Select your Personal Folders service and choose Remove to remove the old service
Select Add...
Choose "Personal Folders" in the Add Service dialog box and click OK
In the Create/Open dialog box, locate the folder where you copied your personal store
Click OK
Click OK again to close the Services dialog box
The next time you start Outlook, it may give you a message asking you if you want to change the location of your various shortcuts. (I can't remember the exact wording of the message. Sorry.) You should answer yes to have Outlook update your shortcuts to refer to your new personal store.
Hope this makes sense.
[EDIT] Please note that these instructions pertain to Outlook and not Outlook Express.