Synchronizing e-shop / brick and mortar inventory

You can use that yes with a CSV file.
Otherwise, you can also create your own plugin in order to pull/push data directly from/to the brick and mortar inventory system. It depends on the possibilities of that inventory system...

You can already create orders, add products to them and print them in the back end. There is room for improvement in that interface and yes, we want to improve it in the future so that it's easier to create orders. But we want add another specific view for it.

My previous message also answer the other half of the problem. You want to update the inventory after a purchase in Hikashop:

Otherwise, you can also create your own plugin in order to pull/push data directly from/to the brick and mortar inventory system

If you create a hikashop plugin with the onAfterOrderUpdate trigger, you can contact the inventory system to transfer the information of the order. That event of HikaShop's API is even documented on our website. The question is more on how you can contact the inventory system. And I can't answer that as that depends on the inventory system, not HikaShop.