British chemist John Dalton first proposed an atomic theory based on scientific evidence such as conservation of mass and the definite elemental composition of compounds.

It is a metathesis or double replacement reaction yielding barium sulfate and magnesium hydroxide. The interesting thing about this reaction is that both products are insoluble in water though both reactants are soluble. Usually there is only one insoluble product, the other metathesis product is soluble.

Because the two ions are necessarily produced in exactly equal amounts.

Use differences in their properties.  For example which is the only one of these which is soluble in water.

None.  A mixture requires at least two substances.  A molecule is the particle of only one substance.  Elements and compounds can both exist as molecules.  Neither compounds nor mixtures are necessarily molecular.  There is no definite relationship between these terms.