Well, I can answer the part about the fan speeds.

The fan in front of the rad does not come on simply because you press the AC button.

When the refrigerant pressure reaches a certain level, the pressure switch on the drier turns the fans on low speed.

Hi-speed is activated by a switch in the cylinder head when the engine temp reaches 100' C or so.

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2012 E350
2006 Callaway SC560