@Andrew since you don’t seem to have much electronics hardware experience, may I suggest you get an Arduino kit from Adafruit.com and do some of their Learning excercises before going further with Donkey Car? Find a kit which has a button included and a POT. Then you can use the Learning examples to understand a bit about electronic wiring, battery power, button switches and servos.
I would start with making the onboard LED blink, then blink with a button push. Then make it dim and bright based on the POT(variable resistor). When you finish that, you should have a handle on doing the PCA9685 Learning example and should even be able to control the steering servo on your car with control via the POT.
Trying to approach this project as a step-by-step project without understanding what’s going on at the basic level is going to result in failure and frustration. If not now, when something breaks.
And yes, if you plug in your ESC control and then put 7.4+ volts also into the PCA9685 you’ll likely burn up your ESC or it’s BEC.