Please use correct units. Kw is power. Kwh is energy. We're talking about energy. Also amps and amp hours are different.

100Ah * 375V = 37,500Wh of energy

200Ah * 144V = 28,800Wh of energy

Completely different energy packs.

Also, 3C discharge on 100Ah cells is 300A. 2C is 200A. It's a multiplier of the Ah capacity of the cell.

If you have a 100Ah pack at 375V, and you discharge at 3C, that's 300A. The voltage will sag a little bit, lets say 12%, so down to 330V. That would be 99,000Kw of power. With a 37kwh pack, you should have no problem with power using 100Ah cells that can discharge at 3C. But realize, discharging at 1C would give you 37kwh of energy. Discharging at 3C, you'd need a larger pack to get 37,500kwh out. The higher the current you discharge, the less energy you get out of the cell.... so expect to get a larger pack to get 37kwh out. Something with at least 20% more energy at 1C.

Basically, you're going to be spending a lot of money on this vehicle to get that range, so be sure you are sold on the idea, because it's a lot of work and lots of time.

The controller regulates voltage and current to the motor, yes.