Hey there, @modernfamilylaw.
I'm happy to provide some insight into manually tracking invoices.
While the system can track invoices sent directly from QuickBooks, the ones sent through a PDF will have to be manually marked as Sent. You can do this by using the Message feature and adding notes there.
As for paying the transactions, you can click Mark as Paid to the right of the invoice details in your Transaction list. I've included a screenshot below to show you where that option is.
Please know I'm only a post away if you need anything else. Have a great day!