Thank you for reaching out about this. Generally speaking, the gift card emails should be sent as soon as the order is marked as fulfilled. You can choose whether or not gift card orders are automatically fulfilled in your admin under Settings > Checkout.
For the GC orders where an email was not sent, are these order showing as fulfilled or unfulfilled in your admin? If they are showing as unfulfilled, then you will want to try fulfilling the order to have the email be sent out. If the order is showing as fulfilled, but no email was sent, then please reach out to our authenticated support team for further assistance with this. To access our authenticated support, please follow this link: Shopify Help Center and type “contact support” into the chat box.
When you add a customer profile you should then see a check box that says “send gift card now”, when you select that and finish making the gift card product then an email should be automatically sent.