RE is reverse engineering. But if you already have the schematic, then there is obviously no need to do that.
Yes, TR1 is there to drive main switching transistors (that's what makes this a switching power supply). TR2 is a main transformer that actually handles the load.
IC1 takes feedback voltage from the unregulated output through D5 and adjusts switching frequency accordingly.
Unregulated voltage goes to power the fan, and 7808 provides linear regulation for the output voltage.