Thank you for sharing your screenshots of what you are seeing and I am glad to hear you started troubleshooting this issue already.
If the areas I noted don’t seem to be the root cause of the checkout issues I would ask that you please reach out to our live support for additional help. They will be able to go through your shipping settings and product details once they authenticate your account access and also loop in our Shipping support if needed.
To contact our live support please follow this link: Shopify Help Center - Contact Support, sign into your store account, search for “Customers can’t check out, no shipping rates” and use the contact support button at the bottom of the search results to see all our live support options.