The noise might be the fuel pumping through the rails, air pump filling the rear springs, a fluttering relay, or ??
You better have someone else turn the key on, while you have your head under the hood.
White smoke !! Is it smoke, or steam?
Smoke might be valve stem seals are shot, steam might be it's freakin cold outside.
Shuts off at idle, can be alot of things, or combination of things. You would do well to eliminate one system at a time.
* Plugs and Wires
* Fuel Filter
* Air Filter
* Check Battery condition, and connections.
* Check coil(s) condition, and connections.
*** You get the picture