The foundation is concrete and these are the stairs that lead to the living/dining & Kitchen open plan room.

You'll need to find out what is under the tile. I'm a little skeptical due to the stairs. If you're planning to tear out the tile, go into a closet and bust out a tile in a corner. If it's concrete then you're set. If a cement board is down then you can not do stained concrete in that area.

I live in Malta, we don't use wood in none of the building material. The material used is limestone and concrete. Don't know if that information helps.

Yes, helps enormously. What a beautiful area you live in, have always
wanted to visit and see the many sights and attractions. With that being
known you shouldn't have any problems with stained concrete. Just keep
in mind that if you ever decide later to have tile or wood installed in
the home over the stained concrete..the finish on the concrete will have
to be removed prior to and it will be hell.

Thanks for the feedback. I have looked into the tile mimic concrete flooring. That could be another option and I assume would cost cheaper? I also plan to change the beige color walls to a light grey color. I think it would look better especially along the staircase.

After ready so many people's issues with finished concrete, I would look at large format concrete "looking" porcelain tile. It is extremely handsome and much more durable (less prone to scratching) than finished concrete itself.