Can the 'Processing Order' & 'Completed Order' emails be disabled since we sell intangible items which do not get shipped at all?

Yes. You can disable “Processing Order” emails (under WooCommerce > Settings > Emails > Processing Order) and Proforma invoices (under WooCommerce > PDF Invoices > General Settings). Then your customers would only receive email/invoice once their order is completed (payment rendered).

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