Verified answer

Black smoke?

Too much gas.

Could be simple.

Get a second opinion at another shop.

Not going into reverse has nothing to do with the engine, it would be a transmission problem.

Black smoke usually indicates a clogged air cleaner.

White smoke is usually a fuel problem, or coolant in the exhaust.

Blue smoke is burning oil.

The most basic tests for an engine are;

Compression test, to make sure all cylinders are not leaking and are equal.

Compression leak down test, to determine where the leaks in the cylinders are. (Valves, rings etc)

Vacuum test for intake gaskets and valves.

Oil pressure test to see if the oil pump is working properly or if the bearings are worn out.

Combustion gas test on the radiator can detect minute head gasket leaks.

To rule out any potential problems with the engine, most mechanics will place the car on dialysis--basically what it is is it's hooking the engine up to a machine, allowing the mechanic to detect any problems with the engine. I had a lot of problems with the engine with a car I used to drive, and when they placed the engine on dialysis, they found out the catalytic converter was bad.

A "compression leak-down test" will quickly identify many major engine problems.