why's there unequal distribution of kinetic energy in water molecules?
Because that's the way it is - there is always some distribution of energies of molecules, it doesn't hold for water only. Molecules collide all the time, partially exchanging their kinetic energies. Some get faster, some get slower in the process. Total energy stays constant, but individual speeds/energies don't.
See for example https://en.wikipedia.org/wiki/Maxwell–Boltzmann_statistics
Why do the surface molecules have more kinetic energy than the other molecules?
Why do you think they do?
Is this even true in the first place? If anything would expect surface molecules to have a lower temperature because of evaporative cooling.
I think because the lower bulk of water is not free to move around and due to movement hindrance by the upper molecules their energy gets transfered to the surface.
Nope - if anything, the more pronounced effect will be the one suggested by Ygg.
There exists a phenomenon called surface energy, and yes, the total energy of a molecule on the surface is slightly different from the total energy of a molecule in the bulk. But the difference is pretty small and not directly related to the kinetic energy of the molecules. As a first approximation (and a quite good one), average kinetic energy of the molecule doesn't depend on whether it is in the bulk or on the surface.
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