||Let (X, omega(0)) be a compact complex manifold of complex dimension n endowed with a Hermitian metric omega(0). The Chern-Yamabe problem is to find a conformal metric of omega(0) such that its Chern scalar curvature is constant. As a generalization of the Chern-Yamabe problem, we study the problem of prescribing Chern scalar curvature. We then estimate the first nonzero eigenvalue of Hodge-de Rham Laplacian of (X, omega(0)). On the other hand, we prove a version of conformal Schwarz lemma on (X, omega(0)). All these are achieved by using geometric flows related to the Chern-Yamabe flow. Finally, we prove the backwards uniqueness of the Chern-Yamabe flow.