How do you show/hide delete(remove) product button in the Cart?
Shopping cart in Drupal commerce is a view. To remove the "remove" link, all you need to do is edit it and remove the "remove" field.

The view can be found at /admin/structure/views/view/commerce_cart_form/edit
and remove the field (Line items referenced by commerce_line_items) Commerce Line Item: Delete button (Remove)