Why is my car shaking and the check engine light flashing?
A shaking vehicle AND flashing MIL ("check engine light") sound like the vehicle is misfiring on at least one cylinder. As @Anna Nguyen, @Brendan Sinclair, @Antoun Nabhan and others have said, it could be an ignition related problem. It could also be fuel-related. If one or more fuel injectors are clogged or dead, that would also cause a misfire in the affected cylinder(s). These are relatively cheap/easy things to check and fix.Other causes (which could be more complicated and more expensive) to fix include contaminated fuel, a bent intake or exhaust valve, a broken valve spring, a damaged piston/connecting rod, and on and on.I recommend getting a scan tool and checking the codes which are causing the MIL to light/flash and I also strongly recommend NOT driving the vehicle until the problem is fixed. If you continue to drive the vehicle as is, you will exacerbate the problem. Dumping unburned fuel into the exhaust due to a misfire will overheat and kill your catalytic converter. A more serious problem like a bent valve can eventually cause you to crater your engine (i.e.: completely destroy the engine).
Is it natural for an old diesel vehicle to blow black smoke on acceleration? Or is this a sign of a worn engine?
This is soot. It occurs when too much fuel is injected into the combustion chamber for it to burn completely.In older engines, the fuel system will make assumptions about how well the engine is breathing and the maximum injection volume will be tuned accordingly. If the engine has trouble breathing, e.g. due to a clogged air filter, the assumption will be wrong.Modern engines have control units that actively measure air mass and make appropriate adjustments.