Dear Mansario,
Happy new year. There are lots of questions in this thread, I am trying to answer them one by one.
Q1) I would like to use the same taxonomy in the posts and the products, it will allow me among other things to display the products related to the posts
Yes, it is possible to share the same taxonomy to multiple post types, see our document:
https://toolset.com/documentation/user-guides/create-custom-taxonomies/#3-select-post-types
You can connect the taxonomy to other post types. Using the same taxonomy for different types will allow you to connect between them and create advanced content displays on the site’s front-end.
Screenshot:
hidden link
Q2) I want to customize my single posts, my archives and restrict archives to categories and regions chosen by the registered user in his profile
Yes, it is possible to customize single posts and archives pages, see our document:
For example, you can customize single post with Views content template:
https://toolset.com/documentation/user-guides/setting-view-templates-for-single-pages/
And customize archive page with Views wordpress archive:
https://toolset.com/documentation/user-guides/creating-wordpress-custom-post-archives/
For the question "restrict archives to categories and regions chosen by the registered user in his profile":
It depends on how do you setup the "regions chosen by the registered user in his profile", if the "regions" is a custom user field, you can get the "regions" field value with Views shortcode
https://toolset.com/documentation/user-guides/views-shortcodes/#wpv-user
And pass the field value to shortcode [wpv-conditional], check if current post has specific term, then display what you want, for example:
https://toolset.com/documentation/user-guides/conditional-html-output-in-views/displaying-taxonomies-conditionally/#specific
Q3) i would like to manage different types of users and sellers with different roles and different types of products
You can setup custom user roles with Access plugin:
https://toolset.com/documentation/user-guides/managing-wordpress-admin-capabilities-access/
And specific each user role's access to custom post types:
https://toolset.com/documentation/user-guides/setting-access-control/
Q4) I would like to highlight/rank products according to the options subscribed by the advertiser/seller
Similar as Q2), you can use shortcode [wpv-conditional] to check if it is a highlight/rank products according to the options subscribed by the advertiser/seller, and display what you want.
Q5) I would like to set up a complete and dynamic search interface based on my taxonomy and the choices/subscriptions of registered users
You can setup the custom search form and search result with Views plugin, see our document:
https://toolset.com/documentation/user-guides/front-page-filters/
Custom search form supports query posts, taxonomy filter and custom post fields filter, but it does not support query users yet.
Q6) According to the geocalisation of the IP address of the visitor, I would like to be able to restrict by default the view of this visitor to articles and products associated with the region of his IP address
There isn't such a built-in (IP address) feature within Toolset plugins, but Toolset map plugin supports the Distance filter by user's location, see our document:
https://toolset.com/documentation/user-guides/display-on-google-maps/filtering-and-ordering-map-markers-by-distance/
Filtering and Ordering Map Markers by Distance
Q7) I wonder (I did, however, check, but without success) if it is possible and above all viable to set up a taxonomy where a category can have several parents
No, this is not possible within WordPress taxonomy, in hierarchical custom taxonomy, one term can only have one parent term, just like WordPress built-in taxonomy "Category".
In your case, it needs many-to-many relationship, you might consider the many-to-many relationship between post types, see our document:
https://toolset.com/documentation/post-relationships/
If there is any new question, new ticket please, that will help other users to find the answers.