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

You will find the Balance in the order details view.

The positive balance is displayed in black. This means that the customer has overpaid this amount.

The negative balance is displayed in red. This means that the customer still needs to pay this amount.

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

You can view all transactions on the Payments tab.

You also can show the balance in tables. See how to configure the table here.