Check engine light turned on after replacing the crank sensor

It sounds like you have a blown head gasket which will explain the white smoke coming from the exhaust pipe. Here is a guide to help you confirm the head gasket failure, some checks you can do with no equipment or tools:

https://www.2carpros.com/articles/head-gasket-blown-test

Check this guide and video out. Please run down these guides and report back.

Good job, the plug with the black carbon can be from a stuck fuel injector which can cause white smoke as well. Here is how to check the fuel injector:

https://www.2carpros.com/articles/how-to-test-a-fuel-injector

Which cylinder had the black plug?

Yes, that's a sign you have a stuck fuel injector. Did you check for a blown head gasket? Also does the engine use coolant. Here is how you can remove the injectors for testing, check the diagrams below:

REMOVE OR DISCONNECT:

NOTE: Use care in removing injectors to Prevent damage to the electrical connector pins on the injector, and the nozzle. The fuel injector is serviced as a complete assembly only. Since it is an electrical component, it should not be immersed in any type of cleaner.

1. Negative battery terminal.
2. Relieve fuel system pressure.
3. Intake manifold plenum.
4. Fuel rail assembly.

DISASSEMBLE:
1. Injector retainer clip and discard.
2. MPFI injector assembly.
3. Injector O-ring seals from both ends of injector and discard.

IMPORTANT: Each injector is calibrated for a specific flow rate. When replacing fuel injectors, order replacements with the identical part number as the old injectors.

ASSEMBLE:

1. Lubricate new injector O-ring seals with clean engine oil, and install on injector assembly.
2. New injector retainer clips on injector assembly. Position open end of clip facing injector electrical connector.
3. MPFI injector assembly into fuel rail injector socket with electrical connectors facing outward. Push in far enough to engage retainer clip with machined slots on rail socket.

INSTALL OR CONNECT:

1. Fuel rail assembly.
2. Intake manifold plenum.

Check out the diagrams (below). Please let us know what you find. We are interested to see what it is.

You can try it one at a time and then stop if you find a bad one.

Thanks for the video it is showing code #43 which is Knock sensor or electronic spark control circuit fault. This can be the ignition module causing the issue.

I have seen the crank sensors be a problem and the ignition modules. Can you upload the engine making the noise so I can see what it is?

That would be great. :)

Thanks for the video, it seems like it is running okay, with that many miles the engine will be a little noisy. I would try changing the oil with a filter and add in some Lucas oil treatment. Also do you have an oil pressure light or gauge? You could have low oil pressure which means the oil pump pick up might be clogged.

This guide can help:

https://www.2carpros.com/articles/how-to-change-engine-oil-and-filter

Please run down this guide and report back.