Protein surface hydration is fundamental to its structural stability and flexibility, and water-protein fluctuations are essential to biological function. Here, we report a systematic global mapping of water motions in the hydration layer around a model protein of apomyoglobin in both native and molten globule states. With site-directed mutagenesis, we use intrinsic tryptophan as a local optical probe to scan the protein surface one at a time with single-site specificity. With femtosecond resolution, we examined 16 mutants in two states and observed two types of water-network relaxation with distinct energy and time distributions. The first water motion results from the local collective hydrogen-bond network relaxation and occurs in a few picoseconds. The initial hindered motions, observed in bulk water in femtoseconds, are highly suppressed and drastically slow down due to structured water-network collectivity in the layer. The second water-network relaxation unambiguously results from the lateral cooperative rearrangements in the inner hydration shell and occurs in tens to hundreds of picoseconds. Significantly, this longtime dynamics is the coupled interfacial water-protein motions and is the direct measurement of such cooperative fluctuations. These local protein motions, although highly constrained, are necessary to assist the longtime water-network relaxation. A series of correlations of hydrating water dynamics and coupled fluctuations with local protein's chemical and structural properties were observed. These results are significant and reveal various water behaviors in the hydration layer with wide heterogeneity. We defined a solvation speed and an angular speed to quantify the water-network rigidity and local protein flexibility, respectively. We also observed that the dynamic hydration layer extends to more than 10 angstrom. Finally, from native to molten globule states, the hydration water networks loosen up, and the protein locally becomes more flexible with larger global plasticity and partial unfolding.