Sound like your IAC valve might be sticking. This has happend to a lot of other people too. Also check the wiring to the Crank shaft position sensor and the sensor itself might be going.
As for the no-start restart, are you getting a CEL?
I had a problem with a warm engine nostart with a misfire.
Car would run great, if I turned it off and let it sit once warm, restart was impossible till it cooled down.
Here's link to the post just incase.
Linky 
