Glass absorbs light where there is something in the glass that can resonate at the frequency/energy of that light.
It depends on exactly how UV you mean, at very short wavelength UV you can interact directly with the outer electrons, but at more typical 200-350nm you are mostly being absorbed by the inter atomic bonds in the glass. Unfortunately a lot of this is influenced by trace heavy metals and impurities so it's difficult to predict (and control)
There is a Schott datasheet explaining this
Q2: Darker colours fade faster because they have more dye and the change is more visible - it's hard to see when white paper has faded!
Dyes work by absorbing certain colours of light, so a red dye will absorb blue and green light to only allow red to reach your eye. When it absorbs the green and blue photons their energy must go somewhere mostly to heat, that's why dark cars or clothes get hotter on a sunny day. But some of the photon's energy will break the chemical bonds in the dye and so gradually reduces it's effectiveness = fading.
I disagree with the premise of this question. Using DC permittivity and DC resistivity is an awful starting point if you want to understand anything about visible-light response. [Update: I should say that it's not that bad a starting point for metals specifically. Much worse for other materials.] When electrons move back and forth at 60 Hz, they usually move in a totally different way than when they move back and forth at 1 quadrillion Hz.
For example, in an n-type semiconductor, at 60 Hz, the conductance comes from electrons in the conduction band getting shifted within the band and traveling and sometimes bumping into defects. The conductance at 1 quadrillion Hz comes from electrons in the valence band being pulled into a quantum superposition state between valence and conduction band states. The superposition state happens to jiggle back and forth (by atomic-scale distances) at 1 quadrillion Hz, because of the energy difference between the two states and the laws of quantum mechanics. Soon the superposition is disturbed and you get an electron-hole pair.
For example, rubber has a very high resistivity but is not transparent. Indium-tin-oxide has a low resistivity but is transparent.
To understand visible absorption, you need to be thinking about energy levels and modes, not DC resistivity.
Water absorbs visible light because of various weak (harmonic) vibrational modes. Normally, vibration modes are only in the infrared, but water has unusually high-frequency vibration modes that reach just a bit into the visible. (Because hydrogen is light and bonds very tightly to oxygen. Just like a taut thin string on a guitar will vibrate at a higher frequency than a loose thick string.) Glass does not have that property.
Glass can be much more transparent than water: For example, fiber optics are glass strands through which light can travel many kilometers with negligible absorption. Fiber optics are manufactured very carefully to reduce absorption; if you made ordinary window glass that was 1km thick, it would certainly be opaque.
Best Answer
It depends on what your "glass" is made out of. If you work in a chemistry lab, it's common to use cuvettes made of pure quartz, SiO2, which has a bandgap of 10.2 eV and will very happily pass ultraviolet light. However, most glass is only 80% SiO2 and its the impurities that lower the bandgap.
The "bandgap" is the distance between the ground state of the electrons and the first excited state. A bandgap of 10.2 eV means that jumping that electron from the ground state to the excited state takes 10.2 eV.
A photon that's 10.2 eV has a wavelength of $1.21\times10^{-7} m$, which is UV light. Less energetic light (e.g. blue-to-red) just doesn't have enough energy to kick up that electron. So the photons pass through because they can't be absorbed.
The impurities lower the band gap because they create many different local states for those ground-state electrons. Some of those electrons now have a bigger bandgap, and others have a smaller bandgap. The smaller the bandgap, the higher the chance that a photon passing through will be absorbed.
This is important in, say, water purification plants, where water is passed through quartz sleeves and exposed to UV light.