Is vapour pressure of a liquid solution constant at a given temperature, no matter the size of closed container and amount of liquid taken?
The equilibrium vapor pressure of a compound at a given temperature is an intrinsic property of the compound, meaning it does not depend on variables like volume of the container, quantity of the compound, etc.  Other examples of intrinsic properties include density and melting point. None of these intrinsic properties depends on the quantity of the material or it's physical surroundings.