Both emitters are at ground, so both bases at about 0.7V.
The questions: Is the collector of Q1 also at about 0.7V or is there a voltage drop across the 10k base resistor of Q1 and if so, how to calculate how much? If there's no voltage across the base resistor, why not? (I have measured this with a VM so know the answer in practice but want to understand it.)
Assuming collector of Q1 is also at about 0.7V, the current in the collector of Q1 is a bit less than 1mA (19.3V across 20k).
The rest I think is fairly straightforward: since the bases of both transistors are at the same voltage and have equal value base resistors, the base currents will be the same and therefore so too the collector currents (give or take unintended component differences). So the collector current of Q2 will also be about 1mA, hence the 10k Q2 collector resistor to set the output at the 10V midpoint.
So, the bit I'm struggling to understand is how to analyse what happens across the base resistor of Q1. If I replace both base resistors with 5k, it still seems to work fine.