1995 mystique GS odd noise explained??

[jeremy06]

So I have a 1995, 2.0, auto/air, anyway I have owned this a few weeks and this car has some issues,
1) start-up idle- has high idle at start-up after driving or waiting a few minutes, idle goes down below a 1000rpms but remains a low rough idle?

2) Drive the car for a few miles and the check engine light will come on, and stay on until you shut off the car. once you restart right away engine light will be off and stay off for 20 or so miles. No unusual noises or knocks.

3) My temp guage does NOT work/read, where do I start to track down the problem? Could this be causing my rough idle?