Why are there slots around the transformers in this PCB?
Those slots are isolation between various high-voltage parts of the board. Air is a very good insulator whereas the surface of the PCB can become low resistance in the presence of condensation or moisture. 

The slots ensure that, at least, any current that does flow across the PCB will have a long path and, hence, a much higher resistance than it would otherwise.

Russell McMahon's answer to Creepage distance for PCBs handling line voltage AC? may be of interest.