In an avalanche breakdown, are the electrons that break free under the influence of the applied electric field from the depletion region or outside it?
Also, under reverse bias, how exactly is the internal potential difference widened? (causal mechanism, microscopically) I've always seen it stated but never explained.
Avalanche breakdown is caused by impact ionisation. At very large reverse biases the electric field across the depletion region is so large that electrons gain enough kinetic energy to ionise lattice atoms. This causes a chain reaction as the electrons generated from impact ionisation gain energy from the field and cause more ionisation events. So to answer your question impact ionisation occurs where the electric field is large, in the depletion region.
As for your second point, the widening of the depletion region. Remember that the depletion region is formed by the equilibrium between a drift (field assisted) and diffusion (concentration gradient assisted) currents. In reverse bias the field is increased, which means that the drift current is stronger than at equilibrium (V=0). The drift current pushes electrons and holes away from the depletion region so the depletion region grows in size as reverse bias increases.
