Why do higher frequency waves refract more, both ocean waves and light waves? Also why is energy stored in the frequency as opposed to the wavelength.
The phenomenon you describe is called dispersion. I don't know of a really good intuitive way to describe this, so what follows is necessarily a hand waving description. Cavet emptor.
The light is associated with an oscillating electric field, and assuming the material has a non-zero susceptibility it will cause the electrons in the material to oscillate as well. The oscillation of electrons in the material will have a phase lag compared to the incoming wave, and when you add together the incident wave with all the induced waves you get a resultant wave with a shorter wavelength. Because the frequency is constant this necessarily means a reduced speed, and this is why we get a refractive index greater than one.
The frequency dependance of the refractive index arises because the electrons have a natural oscillation frequency. In a typical material like glass this will correspond to electronic excitations, and will be in the UV. As you increase the frequency of the light and get nearer to this natural frequency the magnitude of the induced oscillations increases, and hence the interaction with the light increases. This is no different from any driven harmonic oscillator. As you pass through the resonance and carry on increasing the frequency the interaction strength, and hence the refractive index will fall again.
So the increase of refractive index with frequency is not a general rule. It depends on the relationship between the frequency of the light and the natural frequencies of the material.
Wavelength is just reciprocal of frequency so second question does not make sense. Light scattering can be seen as absorption and immediate emission. If you look at it like this emission probabilities increase with wavelength since the number of final states increases with frequency (you can arrange a wave in more ways inside a box if it has a short wavelength).