On the frontend when a user goes to their Customer Account page, they have the option to edit their account.
However, there is no place here to edit their billing and shipping addresses. These should be stored in their account so they are automatically populated for each order. And if the customer needs to update either address they should be able to do it from this page.
Please add this ability in the Edit Account page
On the backend, when you edit a customer, it only shows one address area. If you add another address it is exactly same as other address. This is a bug!! also this should be in two areas - shipping address and billing address. OR have the option to assign addresses whether they are shipping or billing.
Also, on the backend the Admin should be able to see and click on all the orders that a customer has made. So under each customer there should be a list of their orders (look at hikashop). Hikashop also have a good feature that enables admin to email the customer.