Now starting when cold, it belches black smoke and runs very roug

Naturally aspirated carburetor with automatic choke.

If youre in winter (northern hemisphere) then the choke will set when you depress accelerator for cold start.

After the engine starts it unloads (opens) the choke slightly. As the engine warms it continues to open the choke until fully open.

Likely the choke is not opening as the engine reaches normal operating temperature and fuel mixture us too rich causing poor combustion and black smoke.

Replaced the Idle Air Control?

white smoke is usually water, grey=oil dark grey=other fluids. with the belching and other symptoms i would be inclined to believe you have a blown head gasket.

Did you take a look at your oil dipstick? Was there any water drops on it? From the limited information you give, it sounds like you could have a blown head gasket.

Check your dipstick and see if you find any signs of coolant on it, If you do, most autoparts stores sell a hydrocarb tester to verify it.

The EGR valve is unservicable........Hope this helps.

CARBURETORS BAD ABOUT AUTOMATIC CHOKE VALVE STICKING CLOSE FLOODING OUT ENGINE.YOU COULD HAVE NEW CARBURETOR IT COULD BE FAULTY.

white smoke usually indicates the engine is burning oil or its burning coolant. when the engine is cold remove the radiator cap and start the vehicle, if it immediately begins to blow air and or coolant from the radiator you most likely have a blown head gasket, if not then remove the oil cap and feel for air coming out. if it blows kinda like a hair dryer then you most likely have a piston ring issue and you are burning oil. either way you may be looking at major surgery to repair.

you have a blown head gasket more than likely or weak starter/alternator

Replace The Throttle Positioning Sensor...When you put Accelerator to the floor ... It rolls the Position Sensor Cam to tell computer etc to put Injectors Etc..into cold start mode...as soon as the motor fires..injectors take over and do their job..The Black smoke is the Extra Gas Put it cylinders to Purge it in a cold Start Mode...Throttle Positioning Sensor..and Yes You Can do It.!!! AutoZone-O'Reillys Etc..Easy Fix !! And Remember Castrol GTX-5-30/ 10-30 !!!
For God Sakes DO NOT Run 5-20 Or 20-50 Tooo Thin- Tooo Thick !! -Thanks-Matthew

on my sorento same problem and its solved vacuum pump on turbo, now ok, sorry for bad english, vacuum membrane is broken