How can I make custom static widgets/areas on my homepage?

Probably you can achieve this easily with the plugin you mentioned, Advanced Custom Fields.

But if you can code a bit, there is a way to easily implement this with no plugin. You can create a metabox with custom fields and attach it to the homepage custom post type, if that’s how you have it set up, or to the page that’s assigned as the front page for your site.

More info on Metaboxex here.

Here is a tutorial on how to create Metaboxes.

I use this great plugin to build metaboxes and theme options, check it out, it’s free and a great tool for any WordPress developer: https://wordpress.org/plugins/option-tree/