We don't have support for custom fields with BigCommerce at this point in time.
New Order trigger is trigging on orders that didn't go through
BigCommerce will send all orders, including orders that are marked as incomplete. BigCommerce considers orders where the user got to the payment page but didn't successfully check out as incomplete. You can read more about that here.
If you only want complete orders to trigger the zap, you can add a filter to your zap that looks like this:
I'm having troubles connecting my BigCommerce account