What is the purpose of the customer registration feature in PS3? The purpose is to allow for easier purchasing of products on your site and keeping track of those purchases. As with most online stores, you will have to register with their site before making purchases.
Is it just to collect contact information for later emailing? That is one reason for this.
Is it required to make a purchase? Yes, a user must register to make a purchase.
If so, does the information find its way into the billing and/or shipping fields during checkout, so the customer does not have to enter it twice? If the user fills out their profile, then the information will be pre-populated in the checkout forms.
I seem to remember reading something about order status in another thread. Can registered customers view their order status or order history after logging in? Yes, a user that has verified their email can check their order history and check the status of your order.
Or is it just for the store owner to view the order history? The store owner will also be able to see the order history of a customer as well.
Is it used to remember a customers preferences, such that purchase recommendations can be made the next time the customer visits the site? There isn't a built in product recommendation setup in PowerStore. You would have to implement this yourself.