I've designed the constant current load portion of this project, which you can see here:

https://www.circuitlab.com/circuit/vpe773/constant-current-load/

If you want to know how it works I describe the circuit in detail on that page, but the gist of it is that a PWM signal determines how much current the load will draw.

This circuit is fairly common, but typically uses an N-channel MOSFET instead of the two transistors I've used. A MOSFET would be problematic for my circuit, because the op-amp would have to output a voltage at least as high as the voltage across R2 plus the threshold voltage of the MOSFET, which is typically around 4V. With a 5V supply, that doesn't give me much room to work with. With two transistors set up as a darlington pair, I only need 1.4V for both transistors instead of 4V, which gives me a lot more breathing room.