Like here I have a vase from somebody, I don’t know yet the height of this vase, but I know this one is small and I like to scale(uniformly) it so the height of it can be exactly 557 mm.

Is it possible that I can do that in Rhino in one Scale or other command? Or I have to measure the height first and calculate a scale factor and input that factor when I scale?

Yes. Run Scale. For the base point, select the center point at the base. For the first reference point, select the center point at the top. For the second reference point, type 557.
-wim