It sounds like you may have multiple problems going on here. One possibility is an intermittent electrical short in the coolant temperature sensor, causing the PCM to try to compensate by changing the fuel mixture, etc., and causing the stalling.
Another possible problem is a head gasket issue. The hard starting, rough running, and stalling sound very much like head gasket issues I have seen.
Have the cooling system pressure checked to see if there are any internal leaks. If not, you will want to focus on an electrical/sensor related issue causing your driveability problems.