Hello,
For Admin
Aare they alerted? How many times?
There is a “Due Date” & “Payment Reminder” feature to handle reminders for pending invoices. If Due Date option is enabled(see due-date.png) then it generates due date for the invoice when invoice is created. It sends payment reminder to user & bcc to admin if the day falls on the due date reminders days(see payment-reminder.png). It sends payment reminders selected days between 0 to 10 days after the due date.
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Can they see invoices that are not paid in the admin area?
Yes, admin user can see all pending invoices in backend Invoicing > Invoices. Admin can also send invoice to customer manually from invoices lists page and invoice edit page.
For the customer
Are they alerted? How many times?
Same as for the admin(see above)
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How easy is it for them to update credit card?
If using PayPal gateway then no need to update credit card at website because payment processed at the PayPal site. Update credit card can be managed at PayPal site.
If using Stripe gateway then it allows to update credit card from Invoice view page at front-end.
Let us know if you have more questions.
Regards,
Kiran