Why do we say Sun curves space and the Earth moves following the geodesic? Why do we say sun curves space even if the Ricci Scalar  for a Schwarzchild metric, the solution of Einsteins Equations for the Sun, is equal to zero.
The Ricci scalar for the constant time slice is also zero.
Can we define curvature using a single quantity? If yes then what is it?
 A: According to the mathematical definition of the curvature, it represents the commutator of covariant derivative. More precisely, $$[\nabla_\mu,\nabla_\nu]A^\rho=R^\rho_{\kappa\mu\nu}A^\kappa$$
Where $R^\rho_{\kappa\mu\nu}$ is the Riemann curvature tensor. It is the single quantity that defines (or represents) the curvature of spacetime. For a spacetime to be completely flat at a point means all the components of $R^\rho_{\kappa\mu\nu}$ to identically vanish there. But there are some less strict criteria for differently defined flatness, e.g. if $R^\rho_{\kappa\rho\nu}\equiv R_{\kappa\nu}=0$ then it's called Ricci-flatness and if $R_{\mu\nu}g^{\mu\nu}\equiv R=0$ then it's called scalar-flatness. But such kinds of flatness don't imply that the spacetime is not curved. As long as the Riemann curvature tensor has non-zero components the spacetime is curved - which can be verified by making a vector parallel transport along a closed curve and seeing that it doesn't match with what it was originally. 
