Sophia here from Shopify. It is important that any orders you've fulfilled are marked as such in your admin.
If your store is reviewed by our team, we may ask for evidence that the orders have been handled and ask that you manually mark orders as Fulfilled if you haven't done so already. If there is tracking information available, you can add a tracking number to each order in the admin. You can also set your own suppliers up as a custom fulfilment service to show that you do have someone fulfilling the orders.
Can you tell me a bit more about the orders? I'm curious to know why you used an app to import the products if you're not fulfilling the orders through those suppliers. Once I have more details, I might be able to provide you with some advice on how to handle fulfillment going forward.
You can manually mark orders as Fulfilled in the Shopify admin by following the steps outlined here.
I agree that you shouldn't be using the app to import products if you're not fulfilling or even using pictures from there. Adding a product manually through the Shopify admin or adding multiple by using a CSV file will work fine in this case.
I strongly recommend looking into setting your supplier up as a custom fulfillment service in the admin. This will notify your supplier when you've marked an order as Fulfilled in your Shopify admin and prompt them to ship the product.
Your orders do need to be marked as Fulfilled once the shipment process has begun. Not only is this helpful for you to differentiate which orders have been handled and which still need to be, but it shows Shopify that you are handling orders appropriately and helps you provide evidence if any of your customers file chargebacks. Ideally tracking information is also added to each order if your supplier provides it.
Let me know if you have any questions about the links I've shared here!