Basic rule of thumb for SEO is: single h1 tag followed by multiple h2, h3, h4 tags. Even this rule of single h1 tag per page is not a requirement when using HMTL5 structure as HTML5 markup allows multiple h1 tags per page.
Regarding shop content being first, what would one want when running a shop website, give its product a priority indexing in the search?
Also, this is not controlled by child theme code or functions – it derived from parent theme and woocommerce plugin in play.
You can remove contents as per requirement and also it is recommended to install a SEO plugin like Yoast SEO for best results.