1) Go to Theme Options > WooCommerce > Single product > Move Product Name In Breadcrumbs > Off.
2) Single product displays the badge depending on the hook that you used. You used the woocommerce_single_product_summary, check this guide about hooks positions https://www.businessbloomer.com/woocommerce-visual-hook-guide-single-product-page/
So, everything is according to your code. If you want to place that over the image use
woocommerce_before_single_product_summary hook. Check label now, please.
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