Create custom front page without adding content I am trying to create a custom welcome front page, it should contain two parts (left block and right block).

Each block has a background image (editor can upload), a logo (1 logo for each block), a description text...

Creating a new content type, is not a good idea in my opinion, because I don't like editors to add as much as they want nodes of that content type, so it should be only one content the editor can edit it each time he want to edit the background or logo...

I am thinking of creating a new setting form for this specific front page content containing those fields in a custom module. In this case, can I use picture module to make the background load a responsive image and not the default one uploaded by the editor ?

Thanks in advance.
In your case, yes you can create settings form, where admin will load background images, logo and enter description. But why you want use picture module? You can define new variables in hook preprocess_page for front page. Where in variable you put url to background image, url to logo, descriptions. After in front page template file, set url background to our block, logo and place descriptions.
Finally add styles to block class or id in css file for align background at the block. For this you can use something like this:

.your-class {
    background: transparent url("path/to/background.jpg") no-repeat scroll 50% 50% / cover;
    width: 100%;
}


background url you add in template. I write path to url in code for quick example, you can place this code in some div, add correct url and see result.