All the widgets of the filtered-nav already have their own class and ids, the categories widget has “widget_product_categories”.
So you can modify css of the widget using
<style>
.widget_product_categories h3 span {color:red}
.widget_product_categories li{color:blue}
</style>
the following widgets ( filter by attributes ) don’t have a unique identifier class but they have a unique id easily find it by right-click-> inspect element I.E:
<style>
.#woocommerce_layered_nav-3 h3 {color:green}
.#woocommerce_layered_nav-3 li {color:gold}
</style>
About changing html it’s more complicated, what we usually do is to create a new widget that conforms to specific needs