Strange tranny problems came come from the Vehicle Speed Sensor, the tranny won't know how fast the car is going so it does some weird WHAM! shifts when they aren't expected. If the car is in too high a gear (like it starts off in 2nd), it will appear to have little power. (Of course if your car doesn't have a 1st gear because the electronic shifting isn't shifting in the tranny, then you are borked.) VSS may not throw a code.
Car dying is probably a stuck or failed idle air control, unless the missing power is from a massive misfire or something. It might also be getting stuck open if you sometimes have high idle. If IAC is the problem, holding down the gas pedal a bit will give enough fuel to start. TPS too, I had a symptom of way too-high idle or dying after compression braking that was fixed by replacing the throttle position sensor.
Fuel supply and pressure should also be checked. It's time to replace the fuel filter if you've never done it, it could be plugged.
