P0420 downstream is fluctuating?

Yep, you nailed it, the catalytic converter is probably bad. You can help confirm this issue by checking out this video.

https://www.youtube.com/watch?v=kNXh1Lphzr4&pp=0gcJCcUKAYcqIYzv

Please go over this guide and get back to us.

Hi Ken,
I checked the temperature: the outlet was hotter than the inlet. Even after wiggling the catalytic converter, no rattle noise.
This car has an upstream AFR sensor and a downstream O2 sensor, could the reading be different for the AFR sensor.

Yes, these readings will be different. Let me know what they are after you warm the engine up and hold the RPM at 1500 while you take the readings.

About 2000 RPM

The last image shows O2 sensor unit in Amperage, here is a video.

Is the engine misfiring? Also, are there any exhaust leaks? I would pull the spark plugs to see if they are black, or if one is black letting us know the system is running rich or if one injector is stuck open. Don't mix the spark plugs and upload an image of them please. Thanks for the images and video they helped. P0420 often means the converter is losing efficiency, but before replacing the cat, verify there are no exhaust leaks and make sure the rear O2 sensor and engine operation are normal.

These are the spark plugs: cylinder 1 to 4, starting from left to right.

Those all look good, so it is not one cylinder causing the issue. The downstream O2 should not fluctuate so I would try replacing it and if that does not help I suspect the cat is bad even though you got good temp readings, you might need to do a manual inspection.

After replacing the downstream o2 sensor, do I have to clear the code, or leave it to clear itself if get fixed?

You need to clear the codes, here is a video to help

https://www.youtube.com/watch?v=ahK_eucFi-k

Please go over this guide and get back to us.

I reset the DTC, then drove it and the light came back on again.
Here are the temperatures of the inlet and the outlet of the catalytic converter.
The outlet is about 20% hotter than the inlet.

That cat seems like it is working. It sounds like you may have a bad ECM. I have seen this before, but lets test the wiring between the downstream sensor and the ECM first, here is a guide to help.

https://www.2carpros.com/articles/how-to-check-wiring

You just need to check the two wires I have marked. Check out the images (below). Please let us know what happens.

I checked the wiring as shown in the images, so the voltage was 1.275V.

Yep, I would swap out the PCM with a used or new unit. Good troubleshooting there.