It may stall and refuse to start if the ignition gets wet.
It will do no harm.
Replace it.
I would guess it's an electrical problem. Perhaps there's a frayed wire or something, that when it gets wet, completes a circuit to turn the lights on.
You should clean it
A car gets its power from the engine, or the motor.
Less traction on a wet road so the stopping distance increases.
Check the inside of the distributor cap. Moisture there will prevent an engine from running. Note that YOUR problem may be something else, but you can start by checking there.
You car has an exhaust system attached to the engine. The exhaust can get to upwards of 300o and then because of that, water that touches that hot metal turns into steam resulting in the "smoke" you are referring to. This also applies to the engine when wet.
takes 3 times for engine to start
Short term, not much. Long term, rust and corrosion sets in.
the motor gets lubricated.