Could be two unrelated problems.
First, the engine dying could be from a loose vacuum hose. My car was doing exactly the same thing. A vacuum line on the back of the engine was so bad it fell apart when replaced.
Time to do some serious vacuum hose replacements. Do them all. It will save you a lot of headaches. Some you should do on your own. Breather hoses on the valve cover and the idle control valve. Do a search on the above. You'll get lots of advice.
As for the ACC control, sounds like a bad solder on the ACC control unit. How are you with a soldering gun? Let us know.
BTW, I had the same ACC problems with my car. Re-soldering the board worked.