Yes (wavelength changes), the speed, however, remains constant. If say you were traveling in a vessel going c/2 and began emitting a ray of light the light would have it's frequency changed or blue shifted. This is because energy is conserved throughout the universe and since the photon cannot exceed the speed of light, it's wavelength changes, resulting in a higher frequency (Doppler effect).
to Your second question, yes but only if energy is applied to the system. Again, energy is conserved in both its "stored" state (matter) and "active" state (energy, electromagnetic radiation) and can neither be created or destroyed. So if energy was stored as potential kinetic energy in the cohesive and adhesive forces then maybe. but at that attempting to harness this energy would serve to decrease the entropy of the system an therefore halt whatever liquid from spanning more of the universe. so in all entirety no.