I have attached an image with the ideal order flow.
We want to be able
-to have customers choose if the basket is a gift and if so to leave a message to be added.
-to have the customers be able to choose to ship to multiple addresses when they order more than one basket.
-to have the customer be able to choose to pick up the product at the physical store.
-to have a flat rate shipping charge added per basket ordered.
-to be able to use our FedEx account and print shipping labels from the Shopify dashboard to our FedEx Shipping Lable Printer.
ShipperHQ meets your last three criteria! The in-store pickup feature is pretty self-explanatory, and you can assign to only show for certain products if you don't want to offer pickup for everything. Flat rate shipping per basket is also easy to manage, ShipperHQ integrates with FedEx, and will just automatically pass the shipping order information over to whichever label printing provider you decide to use.