Is the black cable positive or negative?

The red one is positive (+), the black one is negative (-). Never connect the red cable to the negative battery terminal or a vehicle with a dead battery.

1. Is black wire live or neutral?

Is black wire live or neutral?

Black wires should always be considered live, so taking proper safety precautions is important to avoid electrocution. This includes shutting off the circuit breaker that supplies the wires you're working on, or shutting down the power to the whole house at the main electrical panel.