Engine problems of the 2005 Hyundai Sonata

I purchased the vehicle used in 12/2005 from a non-Hyundai dealer. I began to notice that the car periodically did not shut off immediately when the key is turned to the off position. It shudders for a few seconds, then goes off. I have contacted the manufacturer and have been to the Hyundai dealer more than 3 times with this complaint beginning February/2006. I also noticed that the car vibrates/revs up when at a red light. This is very irritating since the vibration also goes through to the steering wheel and causes my arms and hands to vibrate also. Initially, I was told that all of this was normal - however I did not experience any of this when I rented the same type of car last year. Then I was told that there is a loose engine mount. I then had two experiences within one week where the car did not start - lights, radio, a/c still came on - but the car did not start. I had to be towed to the dealership. The first time, they changed a relay and the second time, after keeping the car for one week they changed the entire fuse box. I haven't had a problem with the car starting since, however the vibration is getting worse, the car still does not shut off immediately, and now it revs to the point that the car feels like it is trying to pull off before I take my foot off of the brake pedal. I pulled a car history report that revealed that the car failed emissions, had a left door replaced, and had a starter assembly replaced. None of this was disclosed at the time of purchase and was not included on the car history report provided by the selling dealer - otherwise, I would have never purchased the vehicle. When I questioned a residue behind the radio station display panel, I was told by the selling dealer that it could have happened as a result of the aaa inspection since they sometimes take down the dashboard.