Even if the user selects the city from the dropdown menu, it is not being saved in the ad and also the coordinates are not being correctly assigned. This started happening in my web 3/4 weeks ago..

First check if in form, after selection, correct values are selected and there is no other input with same name.
Then try to enable database logs (store them to query.log) and try to publish again.
Then review if you do not have some failed queries.

This is the log. I've confirmed that the city is correctly selected. So the main problem is that it is not stored as City, Community, Country ( Santander, Cantabria, Spain) and then the coordinates are also saved for the same spot in the city in Santander is: 43.4647200000, -3.8044400000

Thanks

Not seen any failed or error query.
Also inserts looks OK.
Check this:
INSERT INTO oslqhq_t_item_location
(fk_i_item_id, fk_c_country_code, s_country, s_country_native, fk_i_region_id, s_region, s_region_native, fk_i_city_id, s_city, s_city_native, s_city_area, s_address, d_coord_lat, d_coord_long, s_zip)
VALUES
(453, 'ES', 'Spain', 'España', NULL, '', NULL, '6109718', 'Santander', NULL, '', 'Calle Argentina 16', '43.4647200000', '-3.8044400000', '39008')
Based on that, osclass sends OK data to database.

Maybe issue could be that region is not populated in query.
means when you filter by region too, it will not work in this case.

I feel like the main issue is that the form is not registering correctly the region in the example, Santander belongs to Cantabria and if I go on to check previous ads that were posted successfully Cantabria was indeed saved. But then as well the coordinates are being get incorrectly, im assuming is because the query on google maps is not being accurate since it is just passing maybe the city and not even the region or address.

The coordinates being assigned to every single post in Santander are 43.4647200000, -3.8044400000 even if the address is correctly saved in the ad.

example: This ad edenlife.es/     subdomain: restaurants/edenred-accepted/la-malinche-santander_i454

Address: SANTANDER, ES C. HERNÁN CORTÉS, 41 39003
The location is being shown 43.4647200000, -3.8044400000,
when the correct coordinates should be. 43.463230450441465, -3.800044419000731

And in the listings admin view I can see that the regions was not saved. Included screenshot. Restaurante Santlivis in the screenshot was edited after published so it showed the correct region, and coordinates and map....

Thanks for your help

Coordinates are from city table.
If you want precise coordinates, you need plugin like openstreetmaps.

How can the coordinates are being gotten from the city table? Many of my prvious ads got the coordinates to the specific place, when published.

When you publish, city is selected and coordinates are empty, Osclass pick coordinates from city table.

OK, but then why is it not getting the correct coordinates from Google maps?

You need to analyze google maps plugin (or map plugin you use) and try to get coordinates based on location you've entered.