Module for customer history

Is there a module I can place in a sidebar where a customer can click and see not only his personal data but also his order history?

No, there is no module for that.
The orders listing and the customer data can only be viewed in the main area of the template via a hikashop cpanel/order menu item.

So just to be clear, there is no way for a customer to log on to HikaShop from the front end and review his order history. Is that correct?

No, that is possible.
As I said, you can do it by creating a menu item of the type hikashop cpanel/order via the joomla menu manager.

However, that is no displayed inside a module. That is displayed in the main area of your template after the user click on the menu item.