In the Web Store mode all orders are saved to the database by default. You can disable this in Products > Settings > General Settings > Shopping Cart, in the Orders section. Check Disable Order Registration to stop saving orders:
All the orders are shown in the Orders admin menu. In the Inquiry Catalog mode the same menu is called Quotes and lists the submitted inquiries.
You can click the order to see all the details.
Customer Details Section
The Customer Details section shows all the checkout fields filled. In the example there are only two fields in the checkout.
You can change all the customer details fields values.
Order Data Section
In the order data column you can edit the payment status. Set it to Pending, Shipped or Complete. A pending order that has received part of the payment is marked as Partial Payment in the orders list.
You can also create a new order in the admin. The Catalog Statistics screen summarizes your orders over time.