Please file one request, report or question each ticket.
This allows us to reply on point and in time, and you to focus on one issue a time.
As well, later, when you or others search for similar issues, it will be much easier to find a solution, if we separate the topics.
So, let's start with one issue here, and I will shortly touch the rest, but if you have more doubts on those topics, I suggest to create a ticket each.
Navigation should be 'chained' as (ie):
Regions>Provinces>Canton's>Parishes (Counties)>Cities>Neighborhood>Restaurants>Vegetarian
This is a BreadCrumb, and Toolset does natively not provide any form of navigation, menu or BreadCrumb.
However, you can for example use YOAST with Toolset:
https://toolset.com/documentation/user-guides/views-shortcodes-for-other-plugins/
how to set 'administrative' (political) hierarchy of navigation (from Region to Neighborhood)
I am not sure what political hierarchy in navigation is, but if you mean the BreadCrumbs, then refer to above answer.
If you refer to a hierarchical and dynamic search, whereas you can for example choose term one of a certain search handle, and then term 2 and 3 of another handle appears, is not possible, and controllable only partially, more about later.
should I set it as category or like fields?
This depends entirely on you and what the plans are to use, display and keep maintained later.
In general, I go like this:
- as less post types as possible
- categorize post types with taxonomies
- add additional repeating informations with fields.
Whenever I think "Should I use a complex field like checkboxes, or a hierarchical Taxonomy" I try to use a Taxonomy.
But that always depends what I want to do with that data later.
You can as example create a list of taxonomy terms belonging to a post with a single shortcode, but you cannot do that for an entire field's Group.
Or, you can search by Taxonomy and Fields in a post view, but you cannot do this in a taxonomy view itself.
Pods is different, and uses different things.
We do not offer to choose options when assigning terms to Posts.
I am not aware that Pods does that, but I do not use that plugin either.
Coming back to your initial request to have a structure like Regions>Provinces>Canton's>Parishes (Counties)>Cities>Neighborhood>Restaurants>Vegetarian, a post relationship makes sense, definitely.
For example you can make restaurants Childs of the Places, so you can then categorize the places with Taxonomies (City, etc).
Did you know that we have a reference site library, where the project you seem to approach is already available, so to be customized?
http://discover-wp.com/
I suggest to look at this 2 sites:
https://discover-wp.com/site-types/travel-destinations/
https://discover-wp.com/site-types/bootstrap-estate-layouts/
It is correct that WordPress taxonomies do not have the feature of limiting input, and Toolset does not add it either.
As well, it is correct that you cannot nest Fields in themselves.
But, to answer your initial question you can not create breadcrumbs with Toolset natively.
You can use another Plugin (YOAST) and use the ShortCode we provide for.
Please let me know if I misunderstood your request, and let's focus on one issue here only, so we can solve it as soon as possible.
For the Structure itself, as far I understand, yes, a Post Relationship, as I explained above would make sense.
Again here for reference:
- A relationship between Restaurants and Locations
- Locations are categorized in Countries and Continents.
- Or, you create more parent post types to categorize your Locations - as it is done in the Real Estate Site I referenced above.