Hi,
about WooCommerce there are commercial addons that add a block to the composer, but the products are selected using filters and cannot be added one by one.
About the delivery problem, you can install an SMTP plugin and use an external SMTP service or a plugin that redirects all the WP emails to a delivery service. There are some commercial addons, as well, to connect Newsletter directly with delivery services via API.
The volume of emails you can send with those external services of course depends on the plan you buy with them.