Stepper motors B and C in your setup both draw more current than the DRV8825 can handle, and trying to control them from the driver could permanently damage it if its current limit is set too high. However, it might be possible to achieve some kind of motion from those two stepper motors with a low (~1.1A) current limit set on the driver. You can learn more about setting the current limit under the "Current limiting" section of the DRV8825's product page.
As for your connections: instead of a single 100uF across your power and ground on your power supply, I recommend adding a capacitor to each DRV8825 across VMOT and GND, close to the board. Also, I am not sure how closely the ground connections in your diagram match what your system will look like, but it would be better to connect the ground from the Nano to the ground from the power supply where the drivers grounds are also connected.