When an order with Printful items is paid, the order screen shows a Made by Printful box with its status.
When it goes
Your Printful setting decides: right away, after your wait, or held until someone clicks Send to Printful. An order is never sent twice, even after a double click or a lost connection. Printful charges your own Printful account; the box shows what Printful charged you (for people who can see store sales).
Shipping and tracking
Printful packs its items in its own box. When Printful ships, the package appears on the order with its tracking number, and your customer gets your usual shipped email and tracking page. When the order also has items you ship yourself, those go in your own package as usual (Ship card, labels and Pirate Ship leave the Printful items out).
At checkout your own shipping prices are the default. You can also add an option priced by Printful: in Settings → Shipping, add a live-rate option and pick a Printful speed. On a cart with your items and Printful items, the shopper pays one shipping price and sees "Arrives in 2 packages". Pickup isn't offered when the cart has a Printful item.
When Printful has a problem
If Printful can't make the order (for example your Printful card was declined) or puts it on hold, the order shows Needs attention: Printful problem, and owners and managers get a bell and an email. Fix it in Printful, then click Try again, or refund your customer from Payment. Nothing is refunded for you.
Canceling and refunding
Canceling or refunding is never blocked. Before Printful starts, canceling here cancels the Printful order too. Once Printful has started making it, the cancel and refund windows warn you that Printful won't refund you for it.