Engine stutters and chugs

Year, make, model, engine, miles?

i'd suggest getting the cylinder compressions checked , black smoke indicates burning oil so could be piston rings , also that would explain lack of throttle response and low revs

Is the engine idle just set a bit low anyway? Can you access the idle adjustment and turn it up a tad? The sluggish drive may be in need of an engine service but a 1.3 is small for this car. Check out online car owner forums to see if others think so to.

Very much sounds like a fuel filter blockage, or it could be a faulty fuel pump, try a filter first, hope this helps

You can in most cases repair this slow speed stall or unstable idle by cleaning the engine throttle valve and the idle speed control valve using a product called CRC Spray Throttle valve cleaner. Spray the cleaner into the air intake of the engine with the hose removed from the throttle body, the engine will try to stall so hold up the idle speed manually. Once you have used up about 1/2 can of the cleaner stall the engine out while spraying and turn the key off, disconnect the negative battery cable for 5 minutes and then reconnect and drive the car for a about 25 miles of varied driving modes. If this doesn't cure the problem you may need the fuel injectors professionally cleaned by the dealer service dept.

sounds like transmission speed sensor is broke and not telling tranny to shift test it with voltmeter

could be fuel starvation when changing over from one fuel to another.end of one/start of another,especially when engine cold and running on richer mixture .answer is only change when car is at normall temp.sorry but this is in the gas convertion manual....

the idle air control valve may be bad or just needs cleaned out. idle air control valve acts the same as a choke. if it is messing up it will cause engine not to run right.

EGR valve, throttle position sensor or idle air valve should all be checked

Here is what you need to do, a cleaning of the intake throttle blade and the idle speed control air-bypass valve, they get full of gunk over the miles and cause idle issues (stalls) like yours,
Get a can of intake cleaner from any local parts store, not carb spray, intake cleaner, it is made by a company called CRC, remove the air intake hose to the engine, hold the idle high so the engine won't stall, then spray the can of cleaner into the intake while keeping the engine running, use at least 1/2 the can, shut down the engine and disconnect the battery for 5 minutes, then restart and complete a number of mixed driving cycles, town, freeway, stop and go etc., after a few days the problem will go away as the system will relearn to the clean intake