Hello,
1) As the title background images of product categories already contains fade-in opacity level, so if you want fade-In on hover then we have to first set styling for fade-out so when someone hover over the image it shown as fade-In otherwise it remains fade-out for this purpose you can use the below CSS code in Theme Settings >> Custom CSS >> global custom CSS:
.tax-product_cat .page-title-default {
opacity: 0.6;
}
.tax-product_cat .page-title-default {
opacity: 1;
}
Result: https://jmp.sh/S5UoGkq
2) Lazy loading is not for specific images it affects all the images on scrolling down.
Best Regards.