What is the purpose of all these resistors and capacitors in this power supply?
Resistors have voltage ratings, as well as power ratings, and in SMT parts these can be surprisingly low. 

Part of the reason for series chains is UL requirements, part is just seeking a high enough voltage rating. 

Network 3 is a rather over complicated snubber to limit primary side voltage excursion as the mosfet turns off (Transformer leakage inductance and output diode recovery time means that you can get a big transient here even in a flyback).

Network 4 is an interesting special case, as it crosses the isolation barrier and is thus extremely safety critical, hence the 4 resistors. The resistor chain just bleeds off any static charge, the cap (Which is a special safety rated one) exists to shunt interference coupled across the transformer by its inter winding capacitance as otherwise this current will find an alternative path probably causing an EMC fail.  

7 is actually two separate feedback circuits, the bit connected to PH1 which is the normal feedback arrangement for voltage control under normal operation, and the stuff around the dual comparator and PH2 that provides over voltage and over temperature shutdown.

9 This resistor controls the turn on speed of the mosfet, the diode ensures the gate discharges quickly to switch the mosfet off rapidly. 

Hope that helps.