Writing Ionic Equation
The statement, "only compounds in aqueous state can be split or dissociated into their ions," is false in a number of ways.


As you state, molten salts are ionic, and there are room-temperature ionic liquids, such as ethylammonium nitrate , $\ce{(C2H5)NH3+·NO3-}$. 
In addition to water, there are other ionic solvents, such as nitromethane, $\ce{CH3NO2}$. Salts in these solvents break up to form ions.
Further, not everything dissolved in water is ionized. Sugar (sucrose), for example, is not ionized.