You always change orders from Shopify in Shopify, not in Pickware. Pickware applies the changes automatically.
Why do removed line items appear with quantity 0x in the order?
If you remove or replace a line item in Shopify, it stays in Pickware with a quantity of 0x. The change has been applied correctly.
To find out what happens when an order changes during picking, see How do I work with fulfillment orders?
Can I change the shipping method afterwards?
Yes, in Shopify. If you change the shipping method of an order in Shopify, Pickware applies the new shipping method automatically, even after the first import. You cannot change the shipping method of an order in Pickware Admin.
You have two options:
Change it in Shopify: Edit the order in Shopify and select a different shipping method. Pickware applies the change to the order. Before you create the shipping label in the WMS App, check that the new shipping method is shown there.
Switch in the WMS App: When you create the shipping label, you can select a different shipping method in the WMS App. To find out how, see How do I create shipping labels? So that the warehouse knows about it, first add a picking instruction: Open the order in Pickware Admin and, in the Detail tab under Custom fields → Instructions, enter a note, e.g. "Please ship with Express". Save the order. The WMS App shows the note during picking.
If the order cannot be edited in Shopify, e.g. because an app imported it, use the WMS App option.
You can find more about picking instructions in How do I add picking and packing instructions to orders?
Can I change the payment method afterwards?
No. Shopify is the leading system for payment. Pickware takes the payment method from Shopify and does not overwrite it. To change the payment method, cancel the order and create it again.
Can I delete orders or shipping methods from Shopify in Pickware?
You cannot delete shipping methods from Shopify in Pickware. If you no longer need a shipping method, set it to inactive under Settings → Shop → Shipping and filter the list of shipping methods by Active.
Why can't I edit an order in Shopify either?
Orders imported by an app, e.g. from a marketplace, generally cannot be edited in Shopify. This is a limitation of Shopify.