Hello,

You can assign the product to any number of categories https://gyazo.com/53684614157a69ce31f16943d24b43f6

Is there an option to show more than one category section in the shop page? (separate category lists) – you can show all the categories in the shop page. You can configure that in Appearance > Customize > Woocommerce

Please add this code to the Theme Settings > Custom CSS > Global:

.widget_product_categories .count {
    vertical-align: top;
}

Best Regards