How does this wall-wart switcher work?
Well done so far. 

R6 is too big to provide all the base bias to U2 in normal oscillation, but it does 'tickle it into life' at start up.

There is no clock because it's self-oscillating. That's what the B1P34 winding is for, through components like D5,8 and R2. This network is disabled when the opto turns on. 

When U2 starts to turn on, the feedback is such that it turns on harder. It stays on with the current growing steadily in B1's inductance. Eventually B1 becomes saturated, when two things happen. U2 collector current increases rapidly as the transformer inductance collapses, and the feedback voltage starts to drop for the same reason. U2 comes out of saturation, and the collector voltage rises rapidly. This is fed back and U2 starts to turn off. The feedback now turns it off harder. U1 takes part in this as well by shorting the BE junction to remove the base charge rapidly. This flyback phase ends eventually when the core has transferred its energy to the secondary. I haven't analysed it completely, but I suspect it's the R6 bias that restarts the whole conduction cycle.

R10 is to pre-bias the zener. Zeners don't have a sharp turn-on curve, they can draw quite a few uA at volts below their rated voltage. R10 keeps the zener well into conduction, so the turn on of the opto is better defined.

This doesn't answer all your questions, but may redirect your investigations. Try redrawing the components around B1P34 to emphasise their feedback role.

Bear in mind that some components' function may not be obvious, if they've been added to reduce EMI for instance.