The previous answers were reasonable, but a lot of what happens at the atomic level is harder to put reasonably. Here are a few relevant points.
First, forget the flowing of old glass. Viscous substances like toffee and tar can flow slowly, but the liquid in glass flows no faster than most crystals "creep". For all practical purposes it is solid. What makes it "liquid" is not that it flows (it doesn't) but that the molecules in the substance are jumbled. Neighbouring molecules are pretty well ordered, but they are jumbled enough that distant neighbours are not ordered relative to each other. Anyone who has been caught in a crowd of people too crushed together to move will have the idea. You will seldom be face to face with anyone, but instead will stand at a reasonably comfortable orientation. You could however be at any orientation relative to someone a few bodies away. If you had been in a military platoon however, everyone would be standing facing the same way, no matter how far apart. That sort of lattice corresponds to a crystalline state.
The reason for the bumps and thicker lower ends of old panes is that that was as neatly as they could make glass by the early techniques of those days, and it was the most convenient orientation to install the panes.
Next. Remember that from this point of view, light is wearing its wave hat; it is not behaving much like particles. It is in effect an alternating electrical and magnetic vibration of a field. Squeezing between atoms, or between the components of atoms does not enter into the process. Even if it did, the wavelengths of visible light are hugely, thousands or millions of times greater than the components under discussion.
For light to get through glass is not like weevils squeezing between grain kernels, but rather like sound getting through glass; it doesn't squeeze through; it rides through in the interactions of the glass molecules.
Because the light vibrations are changes in electromagnetic fields, they interact with any electric particles they meet on the way. If the particles could move in such a way as to be shaken by the light, then moving them would either absorb the light's energy, swallowing up the wave, so to speak, or send a copy of the wave back like an echo, reflecting the light. Those sorts of effects are what one might expect from electrical conductors like metals. Other sorts of conductors like salt solutions do pass visible light, but they are not transparent to various other wavelengths.
Transparent glass however, does not have electric charges that move at the right frequency to interfere with the wavelengths of visible light, so the electromagnetic vibrations pass through without much interference of the type that we find in metals. (The interference of refraction etc is another matter.)
