Using a TIP120 Darlington transistor to control a 12V fan from an ESP32 board
Bipolar transistors switch on from a current, not a voltage. As this is a NPN darlington, any positive voltage more than a few hundred millivolt will lead to a positive current into the base and a voltage higher than it's VCE will make the transistor turn on fully.
It's there so the transistor base doesn't burn out from overcurrent.
Yes. Yes. You have to connect the grounds so the current can flow back to its source.