Molecular dynamics (MD) simulations have been performed to investigate the shear dynamics of hydration layers of the thickness of D=0.61-2.44 nm confined between two mica surfaces. Emphases are placed on the external shear response and internal relaxation properties of aqueous films. For D=0.92-2.44 nm liquid phase, the shear responses are fluidic and similar to those observed in surface force balance experiments [U. Raviv and J. Klein, Science 297, 1540 (2002)]. However, for the bilayer ice (D=0.61 nm) [Y. S. Leng and P. T. Cummings, J. Chem. Phys. 124, 74711 (2006)] significant shear enhancement and shear thinning over a wide range of shear rates in MD regime are observed. The rotational relaxation time of water molecules in this bilayer ice is found to be as high as 0.017 ms (10(-5) s). Extrapolating the shear rate to the inverse of this longest relaxation time, we obtain a very high shear viscosity for the bilayer ice, which is also observed quite recently for D< or =0.6+/-0.3 nm hydration layers [H. Sakuma et al., Phys. Rev. Lett. 96, 46104 (2006)]. We further investigate the boundary slip of water molecules and hydrated K(+) ions and concluded that no-slip boundary condition should hold for aqueous salt solution under extreme confinement between hydrophilic mica surfaces, provided that the confined film is of Newtonian fluid.