Black smoke coming out of the exhaust

Black smoke = excess fuel. Could be high fuel pressure, stuck open injector(s), fuel pressure regulator failure. I would start with a pressure test as a starting point.

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

Without testing it could be a variety of things. Did the black smoke issue get repaired before the overheating or did it just run that way until it died? If the coolant level is OK then it either has a water pump issue, the fan failed or there is an internal engine failure like a head gasket.

Does it turn over but not run or?

Not if the impeller failed. It just wouldn't move the water.
Was it just black smoke or actual grit and pieces? If it was that it could be that the converter(s) failed and are plugged up. That would also cause it to overheat because the exhaust would be blocked.

Run a back pressure test on the system. A quick method to see if it is blocked is to disconnect the exhaust at the manifolds and see if it runs better.
https://www.2carpros.com/articles/how-to-test-a-catalytic-converter

It all depends on what failed and when. Coolant and excess fuel into the system could easily plug it up fast. I would start there and work my way back to the engine. Black smoke is pretty much always excess fuel through the engine. That can kill a converter quick and the converter could cause overheating. The hard part is knowing if it's worth repairing that engine or just putting in a replacement. That all depends on what you find with the fuel and exhaust systems.

One plug missing wouldn't cause it to be this bad.