I understand that:
- Your key reason for not considering a content type is that you wish
only one of this content type to be added to the site.
- It is the intention that all of the content for the homepage is to be editable.
I would suggest that using a content type may still be a suitable approach: by virtue of not granting any role the "create new [content type x] permission", you ensure that the only type of user who could add new homepages would be the "administrator role" which you have set - a role which you won't have given to content editors.
For the blocks with background images, you might wish to consider use of the field_collection module to create sets of grouped fields; you can template field collections, allowing you to create an element with a background image and other field outputs contained within that element, for example. Ref http://www.drupalcontrib.org/api/drupal/contributions!field_collection!field-collection-item.tpl.php/7 for templating a field collection item. (If you prefer to use the paragraphs module, an equivalent approach would apply.)
The key thing here is that when you create your templates, you can output the file names of the editor-uploaded background images (e.g. a small inline CSS block), and ensure that you make use of the background-size property (you want "cover"). Set the position of the background images depending on how you'd like the visual effect of the responsive behaviour to work.
- For example, 50% 50% will keep the centre of the image in the centre of the available area, while 0 0 would pin the top left corner to the top left of the area.
(The Picture module is aimed at embedding responsive content images, rather than for background images, so would not help you to achieve what I understand you're trying to do.)