Might this be different in v14 ?

When following your proposed steps:

1) The invoice for the 2 deliverd items (although due = 0), still shows the full down payment, which might led the customer to believe that he will receive money back from us (which is not the case)

But, more importantly:
2) The invoice for the remaining 3 items does not get a down payment line applied, this is just a regular invoice for 3 items

Apologies for the confusion.

Open the invoice for the 2 delivered items.

In the "Payments" section, click on the "Register Payment" button.

In the "Register Payment" wizard, enter the amount of the down payment that should be applied to this invoice. In this case, it should be 200€.

In the "Down Payments" section, click on the "Add an item" button.

In the "Add a Down Payment" wizard, enter the remaining amount of the down payment that should be kept for the second invoice. In this case, it should be 300€.

Click on the "Save" button to add the down payment item.

Click on the "Validate" button to register the payment.

In the "Invoice" form view, you will see that the payment is now registered and the amount due is 0€. The down payment section will now show the remaining 300€ of the down payment.

When creating the second invoice for the remaining 3 items, select the "Deduct down payments" option as usual. The remaining 300€ of the down payment will be automatically applied to this invoice.

By following these steps, you should be able to adjust the down payment on the first invoice, keep the remaining down payment for a second invoice, and avoid confusion for the customer regarding the full down payment amount.