Vehicle Overheat problems of the 2006 Hyundai Tucson

While driving one day, I felt my car shift as if the wheel had slipped, this occurred many times after making a turn. I recently had work done to the front (strut, tie rod, knuckle, ball joint) and am also in need of a wheel alignment. I wondered if this was why, so I called the mechanic back, but he told me that it was my tires. However there is still a fair amount of tread on my tires, so I am not sure if thats really true. Next thing I know, my car accelerated out of nowhere and was almost like driving itself at 20mph (the speed it was stuck on even after slowing down). Also while on the high way it did the same thing-- accelerated on its own and jerked to the right. I had to pretty much hurry and catch the wheel before slamming into another car while on a turn and going about 55mph. At random times it will accelerate and pretty much drive itself while I am driving. I typically have to apply plenty of pressure to the brakes to keep it from rolling while I am stopped. Also I am having an issue with overheating. If I idle too long the car will overheat, even though the tank is full. Even with adding more in, the tank stays where it is, it doesn't overflow. It's almost as if the car is just drinking it but it's not filtering through the hose if that makes sense. Lastly, the car did not want to turn on this evening, after about the 5th time I held it longer than usual and it finally puttered to life reluctantly. I don't feel very safe in this truck anymore.