A free plugin from the WordPress directory puts any of your signup forms on a page or post, as a block or a shortcode. With WooCommerce, buyers who tick a box at checkout join a list of yours with a tag, and each paid order is recorded so you can thank them or find them later.
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Yes. The form is a standard block and a shortcode, so it goes wherever text goes.
No. Forms work on any WordPress site; the checkout box and the orders only appear when WooCommerce is installed.
New products when there are any, and the occasional note about the ones we already make. One click to leave.