"If I don't put in terms for all invoices, past due shopw up immediately."

Of course it does; you either Manual set the due date, manually select the Terms, or assign default terms to the customer as you add them to your file.

And Terms need to be edited to confirm they are set up to do what they got Named. The Name is not factual to what someone defined, if that was not You setting it up.

Changing customer settings now doesn't change existing invoices; go update them to fix them.

And you control the Status Stamp by editing that invoice specific Template. Please see my attachment.