You may have a couple problems. First, the idle sounds like a bad idle air control valve (IAC). It could also be causing the hard cold start. Remove it and check to make sure it is working or carboned. It is responsible for keeping the idle steady.
As far as the hard start in the AM, I would recommend checking fuel pressure drop off. When you turn the key on, it builds pressure. When you run the vehicle, the pressure changes, and when you shut the key, the fuel system should maintain pressure for a period of time (never losing total pressure). When the key is shut, see how long the pressure remains. If it drops to 0 over a short period of time, either you have a fuel leak, leaky injector, or the check valve in the fuel pump is bad.
If you need directions, refer to our home page and select "How To." Go to the checking fuel pressure. There is both directions and a video. You will need a fuel pressure gauge, but most parts stores will lend them to you.
Let me know what you find or if you have other questions.
Joe
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Wednesday, November 17th, 2010 AT 3:42 AM