The choice depends on how much current is needed on the 15V line. If it’s a small amount of current (say less than 100mA), a 7815 linear regulator would do the job. Beyond that the heat dissipation would become significant, and you should use a switching regulator instead.
OpenSprinkler uses half-wave rectifier because of the way it switches solenoids. Specifically, it adopts a simple way to use triacs to switch solenoids, and this requires the triac and power supply to share a common ground. A full-wave rectifier would not work as it does not allow ground sharing.
The R3000 diode was picked partly because it has a higher forward drop voltage (3-4V instead of the typical 0.7V). It’s not really necessary, so all circuits now use the common S1B SMD diode instead.
There is no part list for V1.42+ — you can open the circuit diagram in EagleCAD and export a BOM yourself using EagleCAD’s default bom script.