Well to start with the question is a bit vague. A pulley has nothing to do with
a start operation; a loose pulley may cause the belt not to turn fast enough to charge the battery and that's as far as it goes.
Check your belt tension. If loose tighten it. That's All
Depending on what part of the ecu is bad, yes.
Usually vehicle just stops running with no warning
NO!
crank sensor
Yes , Because it might get damged .
The idler pulley has nothing to do with the brakes. If the idler pulley is bad it could throw or break a belt, and then your engine will stop.
usually when a water pump goes bad your bearing in the pulley on it will start sqealing or your car starts to overheat quite frequently
Yes, one bad cell in a car battery will cause the car not to start.
No
Yes. I have had to replace tensioners for this reason.
yes it will because that controls the fireing off the car and if the bad they will not fire and it will not start
you have a bad car
no
Yes, a bad coil will prevent the ignition from firing and the engine will not start.
Bad starter-we can only speculate
No. A bad starter would cause the car not to start.
Depending on what part of the ecu is bad, yes.