How can I see how much the customer owes me for a specific reservation?

You can find the Balance in the order details view.

A positive balance is shown in black. This indicates that the customer has overpaid this amount.

A negative balance is shown in red. This means the customer still owes this amount.

A zero balance is also displayed in black. This shows that the customer has fully paid for the services.

You can view all transactions on the PAYMENTS tab.

You can also display the balance in tables. Learn how to configure the table here.