Whether the following product architecture fields support variables

Hello,

Yes, you can use Rank Math variables in the schema generator here:
https://rankmath.com/kb/variables-in-seo-title-description/#product-price

If you have a custom value or stored it in a custom field for example, you may need to register it to use in the schema editor:
https://rankmath.com/kb/variables-in-seo-title-description/#how-to-add-custom-variables

Regarding the Schema Type in Titles & Meta, the Product Schema is not an option for your products since it is incomplete. We have integrated with WooCommerce so you can save filling in those details as it automatically fetches the data from your products and fills in the schema.

If you wanted a custom Product Schema to be the default with variables, then you may need Rank Math PRO to create a Schema Template to achieve that:
https://rankmath.com/kb/schema-templates/

Hope that helps.

Hello,

There is no variable for shipping details. Also, the Advanced Editor is only available in the PRO version and the account you have used to open this ticket is a free account. Please share the email address of your PRO account so we can verify your purchase and assist you further.

Looking forward to helping you.

Hello,

To add those properties, you can edit the following filter with the appropriate data for these properties so it gets included in the Product Schema as well: https://rankmath.com/kb/filters-hooks-api-developer/#change-post-schema-data

We have created an example filter that would help add this data and it assumes that the refund policy is only applicable to the USA and that it has a 30-day refund period.

The shipping rate section also assumes a flat fee of 5$ to ship within the United States.

This would need to be changed according to the website specifications but it should be a good starting point:

add_filter( "rank_math/snippet/rich_snippet_product_entity", function( $entity ) {
    // Return policy
    $entity['offers']['hasMerchantReturnPolicy']['@type'] = 'MerchantReturnPolicy';
    $entity['offers']['hasMerchantReturnPolicy']['applicableCountry'] = 'US';
    $entity['offers']['hasMerchantReturnPolicy']['returnPolicyCategory'] = 'https://schema.org/MerchantReturnFiniteReturnWindow';
    $entity['offers']['hasMerchantReturnPolicy']['merchantReturnDays'] = 30;
    $entity['offers']['hasMerchantReturnPolicy']['returnMethod'] = 'https://schema.org/ReturnByMail';
    $entity['offers']['hasMerchantReturnPolicy']['returnFees'] = 'https://schema.org/FreeReturn';

    // Shipping details
    $entity['offers']['shippingDetails']['@type'] = 'OfferShippingDetails';
    $entity['offers']['shippingDetails']['shippingRate']['@type'] = 'MonetaryAmount';
    $entity['offers']['shippingDetails']['shippingRate']['value'] = 5;
    $entity['offers']['shippingDetails']['shippingRate']['currency'] = 'USD';
    $entity['offers']['shippingDetails']['shippingDestination']['@type'] = 'DefinedRegion';
    $entity['offers']['shippingDetails']['shippingDestination']['addressCountry'] = 'US';

    return $entity;
});

Here is a guide you can follow to add the filter:
https://rankmath.com/kb/wordpress-hooks-actions-filters/

Looking forward to helping you.