Before revision:  With a bounded terminal condition and local Lipschitz continuity , we give a simple and streamlined proof for the existence as well as the uniqueness of the solution without using the comparison principle. The properties of locally Lipschitz BSDEs with coefficients in BMO space enable us to show the  strong convergence of a sequence of globally Lipschitz BSDEs to the interested one , which is then used to give sufficient conditions for the Malliavin's differentiability.
After revision:  With a bounded terminal condition and local Lipschitz continuity and the strong convergence of a sequence of globally Lipschitz BSDEs to the interested one , which is then used to give sufficient conditions for the Malliavin's differentiability.