Thank you Christian, I am worried about the extension of this thread, but I have good news.
Don't ask me why, but without apparent reason, I have found a determining clue:
Suddenly, in the dev server, the page showed the markers in the map. I don't know why. Consequently I quickly grabbed the html source code of the page that worked fine, and then copied the URL of that page and refreshed the page in other window. As expected, it didn't show the markers at this second time.
I copied the html source code of that second page that don't show the markers, and compared with the one that showed the markers correctly, line by line.
And I found the clue. The page doesn't show the markers because the rendered position tags (longitude and latitude) are rendered with a comma separator instead of a point separator.
I have created a video for you to show you the difference in the code: hidden link
I can confirm you that the map doesn't work when comma is used as separator for data-markerlat and data-markerlon attributes inside the div of the marker.
For example:
DOES NOT SHOW MARKER
<div style="display:none" class="wpv-addon-maps-marker js-wpv-addon-maps-marker js-wpv-addon-maps-marker-marker-10000027
js-wpv-addon-maps-markerfor-map-ts-test-2" data-marker="marker-10000027" data-markertitle="Ecole de Sophrologie Caycédienne d'Agen"
data-markerfor="map-ts-test-2" data-markerlat="44,1934585" data-markerlon="0,6316555" data-markericon="" data-markericonhover=""
data-streetview="no">
</div>
SHOWS MARKER CORRECTLY
<div style="display:none" class="wpv-addon-maps-marker js-wpv-addon-maps-marker js-wpv-addon-maps-marker-marker-10000027
js-wpv-addon-maps-markerfor-map-ts-test-2" data-marker="marker-10000027" data-markertitle="Ecole de Sophrologie Caycédienne d'Agen"
data-markerfor="map-ts-test-2" data-markerlat="44.1934585" data-markerlon="0.6316555" data-markericon="" data-markericonhover=""
data-streetview="no">
</div>
Do you think why on earth data is shown with a comma instead of a point in our server?
We have no idea why it could be happening. I have done a research on the internet and have found a very interesting page where 8 years ago one person had the same issue (although being a drupal page, I suspect strongly that it has to do with our problem!): hidden link
Thanks, again, Christian,
Mario