I have a customer who had submitted (and resubmitted his order). However, it does not show any payment. He used American Express. Is that an accepted

The Square payment integration accepts American Express cards. I checked your form and I can see that the payment integration is configured correctly. 

Based on the submissions, it is possible that the user did not select a product before submitting the form. It means that the product payment field is blank. Here's a screenshot:

If the order was successful, the product will appear in the submission.

I recommend you to set the product payment field as required. In this way, the form cannot be submitted if the product field is blank. Here's how:

In the Form Builder, right-click the product payment field and then click the "Require" option.

Hope that helps. Thank you.