How does the coupled inductor, capacitor and diode combination work?
It's a TI flybuck, a combination of buck and flyback converters by using the same core for both the buck and flyback.

Pros: simple way to get one more output and also isolation on the flynack output if needed (in this case it's not used due to shared ground).

Cons: big limitations on duty-cycle and poor cross-regulation, hence why there is an LDO downstream of the flyback output.



Vout2 will most likley vary with input voltage and to some extent the load on the buck output (3.3 V), but probably designed to stay above 5 V + the dropput of the LDO over the entire specified input voltage and output current range.

For details on how to design a flybuck converter, I would refer you to TI's guide here: AN-2292 Designing an Isolated Buck (Fly-Buck) Converter (Rev. C)