Can the cash drawer open when an online order's receipt prints, and can I open it without a sale?

Both. Under Settings → Printing & receipts, The cash drawer, tick Open the drawer when an online order's receipt prints, which rides on the receipt copy you print for online orders, and Show this switch in the apps too so the Windows app and an owner signed in on the POS can flip it on the spot. Any POS device, the kitchen screen or the Windows app can open the drawer without a sale from the Open the cash drawer button on its own Settings screen, and Money in, Money out and a waiter's hand-in open it as well. The POS and the counter tab in the docs covers the drawer.