Using 2D molecular dynamics (MD) simulation, the equilibrium and dynamical properties of a gravitationally equilibrated Yukawa liquid are investigated. We observe that due to asymmetry introduced in one direction by gravity, several interesting features arise. For example, for a given value of coupling parameter Γ, screening parameter κ and according to a chosen value of gravitational force g (say in y-direction), the system is seen to exhibit super-, sub- or normal diffusion. Interestingly, x-averaged density profiles, unlike a barotropic fluid, acquire sharp, free surface with scale free linear y-dependence. As can be expected for a system with macroscopic gradients, self-diffusion calculated from Green-Kubo's (GK) formalism does not agree with that obtained from Einstein-Smoluchowski (ES) diffusion. A 2D-angular radial pair correlation function g(r, θ) clearly indicates asymmetric features induced by gravity. We observe that due to compression in y-direction, though in liquid state for all values of gravity considered, the transverse mode is found to be predominant as compared to the longitudinal mode, leading to a novel Anisotropic Solid-like Yukawa liquid (ASYL). In in-homogenous Yukawa liquids studied here, Mach cones are found to be asymmetric. When density gradient direction is set in the direction opposite to gravity, the equilibrium is shown to be unstable to Rayleigh-Taylor (RT) instabilities resulting in transport. Copyright © Cambridge University Press 2014.