I built Lighthouse of Alexandria and thought that my Naval units would get a vision of 5 hexes. But that is not the case. The ship I had still has a vision of 1. I see a little more in the coastal area. Is this the improvement? But that does not clear +5 vision range? What does the bonus means exactly?

The +5 Vision Range is on the lighthouse itself.  The benefits to naval units and transports are +1 Combat Strength and +2 Naval Movement Speed.  (Though I'd also love something like +1 Unit Vision on units too, it's not there).

Thank you for the explanation. I will love also at least +1 vision for units on see. 

Is somewhere good explanation how vision mechanics is working? Every tile has +1 vision range (I didn't find other value see picture below). Why this indication not corresponds to the hex high level?

But back to the cultural wonder. I did a screenshot around the lighthouse and we have still the fog of war. Why?

Because of Fog, an actual one this time. You see the clouded tile of ocean, right in front of ones covered in FoW? That's Fog, you can't see past it no matter what.

It makes sens, thank you DNLH