Cb query issue

Your state field has backquote instead of single quote around the country substitution.

Hmm, thanks, but even with 
SELECT  DISTINCT `country_iso_code2`, `province_name` FROM `#__comprofiler_provinces` WHERE`country_id`= '[cb_country]'

I still does not have any results...

You've access to the backend of our demo site. Simply logic and copy and paste over the settings of those fields.

This is what I'm trying to do. Oviously, I wouldn't post on support forum if I succeded.

It's fully functional on our demo site. My guess is you've miscopied or are missing parameters. Review each parameter and integration tab carefully. You're clearly not just copy and pasting values over otherwise the query errors in your screenshots wouldn't be there. The most important parameters being under the following tabs for both country and state.

Parameters > Query
Parameters > Options
Integrations > CB Core Fields Ajax > General

I really don't know what else to suggest as again we already provide a fully functional demo of this. The only exception is if for country you are not doing region filtering you'll need to remove the following from the query and skip configuring its update on integration parameter.

Fully functionnal with a toal different database structure / field names.
Might be interesting to have a demo functionnal with comprofiler tables updated ?
Because if I copy/paste all values, obviously, it won't work straight away.
That's why I've been very specific with my screenshot also and queries.