Can I get a 1.3 EFI Jimny with a turbo
I vote you have a sticky injector or stuffed fuel pressure regulator. Clouds of rich fuel in the exhaust on startup, sluggish/boggy performance at low revs, and terrible fuel economy (from the looks of it) would seem to indicate really high fuel pressure or an injector problem that's flooding the car.
Pull the plugs and read them -
If they read rich, then you have a clue. Alternatively, get the car to somewhere with a lambda meter (sideband air fuel) and get them to stuff it up the exhaust. I reckon it's going to show uber-rich.
Check the fuel pressure at the rail. If it's not to spec, check the regulator or the return line for kinks, blocking etc. a blocked return line will make the car run crazy rich even if the regulator is fine.
Get the injectors cleaned. Your car is 16 years old - that's a lot of scope for injector failure.
That stuff would 100% create the faults you are seeing all by themselves.
If none of that stuff works/is the problem, then it could be a collection of things that are all contributing - timing (keyway damage etc)+ blocked cat etc, but I'd want to rule out the fuel system first. It's what it feels like to me.
Steve.