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I would not expect a valve cover leak to cause a car to stall. A valve cover leak can fill the spark plug area with oil which can cause rough running.
No. The purge valve is part of the EVAP system. The EVAP system reclaims and burns the gasoline fumes from the fuel tank and prevents the fumes from escaping into the atmosphere. A faulty purge valve would cause the "check engine" to illuminate but not cause the engine of the vehicle to "die".
Start and stall out, possibly. Not start at all, not likely.
Check the EGR valve. It sounds like your EGR valve is staying open. An EGR valve that is open at idle will cause a car to stall. An EGR should be closed at idle and open when you are driving around.
It can if it sticks open at idle.
A bad water pump can cause your car to stall if the bearing has failed or it is causing overheating. A seized bearing will put excessive strain on the engine and stall it out.
no
A fuel pump relay switch can cause your car to stall after starting. A malfunctioning fuel pump relay switch can cause your car to not start at all.
a small evap leak would not cause your car to jerk.
yes it will
No.
No, it will just make the car loud.