Controlling three phase heating element
No, startup is not five times nominal. For a resistive heater there is very little inrush going on and your fuses are time lag anyway. Also, "full curent draw would be 37.5 A" is not correct. You don't sum up the currents in a three phase system.


No need. Forget it. A heating element is not frequecy dependent at all. The voltage ramp up is possible on some VFDs but again, you won't be needing it. 
One or more contactor(s). Also, you absolutely must wire it in series with a thermal cut out fuse/breaker.



EDIT: If you haven't bought the heater already, there is this very neat scheme of spacing your say three banks of heating elements as for example, 2, 4 and 8 kW and by binary addition, you have every combination of 2, 4, 6, 8, 10, 12 and 14 kW available to simplify fine regulation close to your steady state and also decrease the rise rate close to the set point. Also, if one element goes out, it will still work but with a bit more hysteresis. I'm missing the name for this scheme but I'll edit my answer when it turns up. For brewing beer, the temperature is crutial so you don't want to overshoot nor prolong you mash-in more than nessesary.