If a parent makes a partial manual DD payment, will the rest of the amount come out of the parent’s account on the due date?

No. If a parent initiates a manual payment, for instance, if they make a part payment of the total payment due then, the balance amount will not be debited. 

When a manual direct debit payment is triggered by a parent, the auto-debit is prevented by the system. However, a parent can choose to make multiple manual payments using the 'Pay Now' link found in the email.