It would be nice to have an email sent to my customers "automatically" after I click that their payment has been received. This would save me the step of having to go back into the Invoices tab and manually finding their invoice and sending them an email. It would save me a lot of time if it would just queue them the email for me.

Yes, I agree very much !!!!
Same with an actual shipping confirmation email.

Could there at least be an email function that allowed the mass emailing of several customers similar to the "notify winning bidders" function.

Say, if we could select from the entire list of Invoices, any customers using search criteria such as invoice number, auction lot, date, or customer name, address etc.
and send all selected customers a particular email template.
This is easier to program maybe than an automated email, and allows much flexabllity to us as sellers needing to notify our buyers en-mass when we receive payments or ship items.

Please consider this upgrade - it would make AuctionWizard an even more useful seller tool!

The ability to email customers automatically after recording their payment is on our suggestion list. We do not yet have a timeframe for when this might be implemented.

-- The Auction Wizard Team