You should ask them to refund the difference as the 1.5kW VFD is cheaper. They probably just sell them and don't know much about it, as there's nothing wrong with using the 2.2kW VFD with a 1.5kW spindle. Either that or they're trying to cut their losses.

The few seconds delay is normal - it's just to reduce the inrush current when charging the capacitors.

It's very simple to just put a temperature sensor on the heatsink and switch the fan on/off accordingly. You'll probably find it doesn't need to be on that much, since most of the time the spindle (and therefore VFD) won't be operated anywhere near rated current.