Answering your questions one by one...
1.) Is there a reason why I didn't get an email confirmation of the sale or fulfilment? If a sale was completed on your Shopify store, you should have received a notification as long as you have your notifications set up. To make sure they are set up, here are the instructions: New Order Notifications
2.)Is free delivery ever an option? Are you inquiring about free delivery from Printful? If so, this is not the correct place to inquire. You will need to read Printful's help documentation or reach out to them. If you are asking if you can offer your customers free delivery/shipping on your Shopify store, then yes you can. You will just need to adjust your shipping rates in your shipping settings to offer free shipping based on whatever criteria you want to offer. Note that just because you offer free shipping/delivery does not mean that Printful won't still charge you shipping, so you will want to make sure you haver your pricing set up to be able to absorb those costs.
3.)Is there a reason I didn't receive an email confirmation of my purchase or fulfillment? Again, it appears you are inquiring about something from Printful, in which case you will need to look at their help documentation or reach out to them for assistance. Printful is integrated with your Shopify store but it is still a separate company from Shopify.
Here is a link to Printful's Help Center