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.