How can I use exports to find out how many Invoice Past Due emails have been sent out?

Download the Invoices - Summary export (Type: Charge, Status: both Paid and Past Due). The Past Due version is straightforward since the list you download is the total number of invoices that entered the dunning cycle during the selected time period, but for the Paid version of the export, you'll want to go to the "recovery_reason" column and delete all invoices that don't have this field populated since this indicates whether an invoice was once Past Due and later recovered. If it was once Past Due, then you know the Invoice Past Due email was sent.