How to use categories in the URL with Advanced Custom Fields?

For #1, I think what you’re looking to do is add Custom Post Types and Custom Taxonomies, which isn’t possible via Advanced Custom Fields alone. Custom taxonomies are your own versions of either categories or tags.

If you want to use a plugin to create the post types and taxonomies, you could use something like Custom Post Type UI. That would get you where you need to go with the URLs.

For #2, yes, you can have custom templates for each category (aka taxonomy) archive page. You could use taxonomy-your-category-name.php to achieve that. See the full hierarchy list for more details.

You could use these in conjunction with ACF, as well.