You’ll need to contact PayPal with their debug id for details about the error.
As for the notification, make sure the event setting on the notification configuration page is set to one of the payment events such as payment completed. That will prevent the notification being sent until the selected event occurs.
Will the user receive some sort of on-screen notification that the transaction failed? I’m mainly concerned about the user and myself believing an order has been placed when it hasn’t.
Yes, there will be an onscreen notification from PayPal when the transaction does not go through. You are additionally preventing the Notification from being sent until after payment is completed.