A hydrated 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC) lipid membrane is investigated using an all atom molecular dynamics simulation at 308 K to determine the physical sources of universal slow relaxations of hydration layers and length-scale of the spatially heterogeneous dynamics. Continuously residing interface water (IW) molecules hydrogen bonded to different moieties of lipid heads in the membrane are identified. The non-Gaussian parameters of all classes of IW molecules show a cross-over from cage vibration to translational diffusion. A significant non-Gaussianity is observed for the IW molecules exhibiting large length correlations in translational van Hove functions. Two time-scales for the ballistic motions and hopping transitions are obtained from the self intermediate scattering functions of the IW molecules with an additional long relaxation, which disappears for bulk water. The long relaxation time-scales for the IW molecules obtained from the self intermediate scattering functions are in good accordance with the hydrogen bond relaxation time-scales irrespective of the nature of the chemical confinement and the confinement lifetime. Employing a block analysis approach, the length-scale of dynamical heterogeneities is captured from a transition from non-Gaussianity to Gaussianity in van Hove correlation functions of the IW molecules. The heterogeneity length-scale is comparable to the wave-length of the small and weak undulations of the membrane calculated by Fourier transforms of lipid tilts. This opens up a new avenue towards a possible correlation between heterogeneity length-scale and membrane curvature more significant for rippled membranes. Thus, our analyses provide a measure towards the spatio-temporal scale of dynamical heterogeneity of confined water near membranes.