All you GTM Kit settings are set as they should be.
I have tested your site and there are multiple problems. I don’t if they are caused by customizations by you or if your theme does not follow the standard structure.
The add_to_cart event does not fire because the GTM data is not found in the ‘add to cart’ HTML section. GTM Kit is adding this data using the edd_purchase_link_end action hook and if this hook has been removed the data can’t be added,
The begin_checkout event is not fired on the /checkout/ page. GTM Kit uses the EDD function edd_get_option( 'purchase_page' ) to detect if the current page is the Checkout page. It uses edd_get_option( 'confirmation_page', edd_get_option( 'success_page', 0 ) ) to detect if the current page is the confirmation page, which is where the purchase event should be fired.
If the ‘checkout’ and ‘confirmation’ pages are not properly registered in EDD, and thus cannot be detected by the edd_get_option function, the ‘begin_checkout’ and ‘purchase’ events will not be triggered.
Check EDD Settings > General > Pages
