My name is Dallas from the Shopify Social Care Team.
If you wanted to change the price that is just shown on the cart there isn't much that can be done with a simple click of a button. When a price is $0.00 it won't be able to be changed from that. Another alternative recommendation that I could suggest would be to contact the Shopify Experts. However, for a customization like this, it isn't guaranteed that they would be able to adjust this either.
As for the wording on the on the cart page, that can be edited in the language section of the Theme Settings. To get there you would go to your store admin and click on Online Store > Themes > Edit Languages. From there you can type in "your order is free, no payment is required" into the search bar and adjust what you would like it to say from there.
I really hope that this helps to answer your questions! If you have any more questions at all feel free to call us or chat in at any time. Our support is here to help 24/7.