It appears be something related to the orphan pages, since there is no _index.md in this subfolders.
Is it possible to use this kind of structure without moving all my files under the same folder ?

Which section is that the rendering of? You don't need to put a _index.md but blog/ for example doesn't have any pages in it, just a few sections which themselves have pages.
If you want to sort by date though, you will need to add a _index.md in each year folder

The template and output is from the main index.html page.
Is is not possible to iterate over all markdowns recursively ?
I did put a _index.md but the template is still not working, I need to deal with each category individually ? There is no parameter or loop to iterate over everything ?

It appears be possible from this comment

/// Used to create a default index section if there is no _index.md in the root content directory
impl Default for Section {

I did create a content.orphan_pages to access all orphan pages, will send a PR soon.

I did the changes here to access all the pages and it's working as expected from my part.
I did create a post here https://zola.discourse.group/t/add-orphan-pages-in-content/289 before creating the PR.

If you want to access pages from nested sections, you need to mark the nested ones as transparent.

Great, thanks