Elias here with Shopify Support. That’s a great question!
I understand you placed a couple of test orders and did not receive any of the order confirmations or tracking numbers. Since the test orders were processed using cash on delivery (COD), you need to manually mark the order as paid in your admin. Once the order is marked as paid, the order confirmation will be sent to your customers. For your reference, we also have a guide to help with the processing flow for online orders.
The same applies for the tracking number, once you fulfill the order in your admin, you can trigger the shipping notification to be sent to your customers. The shipping notification and tracking is optional, you can choose to send this or not.
Here’s a screenshot of an order from my test store:
I hope this clarifies the order processing and fulfilling orders! Could you take a look to see if you can see the buttons from my screenshot?
Thank you for following up and providing an update on this. I’d be happy to take a closer look and loop in our Technical team. I was able to find your store and I've sent an authentication email to the registered email address we have on file. Kindly check your inbox/spam/junk folder in the account owner's email and reply to it, remember to include the order number of your test order. After that, I’ll be able to take a closer look with our Technical team. Thanks!