Rae from Shopify here. Thank you for reaching out with these questions. I'm happy to lend a hand!
Looking at your question regarding gift wrapping first, there are two different options we can use to install this feature on your site:
In terms of your second question about charging a second delivery fee to customers who miss their first delivery, this can be done directly in your Shopify admin by using a draft order invoice and emailing this invoice to your clients so they can make payment. However, rearranging the delivery time will need to take place via email, over the phone, or through another support method with your team directly, as draft order invoices will just charge the amount of the delivery fee, but don't have the option to reschedule the actual delivery.
Additionally, there are some third party apps that might work to help reschedule your deliveries. I suggest looking into Store Pickup + Delivery and Order Delivery Date to inquire further if these apps offer this feature. It's also a great idea to touch base with the developers of these apps to confirm if this option is included in their integrations.
Please let me know if you have any questions or concerns about the above information and I'll be glad to help further.