Are colligative properties applicable for volatile liquids and gases in liquid solvent? Why/Why not?
Yes, they are, but consider that colligative properties are often described in terms of equations whose derivation require making various assumptions about the substances involved, most importantly that the solvent and its mixtures behave close to ideally (follow Raoult's law), and that the solute does not affect the chemical potential of the solvent in the second phase (solid in freezing point depression or vapor in boiling point elevation). Textbook descriptions of freezing point depression in general assume that the solute does not partition into the solid, for instance, since partitioning would imply formation of a solid solution with a depressed (altered) chemical potential for the solid solvent, a complication too formidable to tackle in an introductory text (and even more advanced ones).