This idea has not occurred to me since the crankshaft position sensor is none contact hall effect sensor, and in a seal environment. It is very difficult to reach, so I am thinking if I remove it, I may as well to replace it. I just have this nagging doubt the problem is really this sensor.

Yes, I have cleared it. Once cleared, it will not reappear until the shifting problem occurs. I have let the engine idle for a over 10 minutes and not seeing any error (crankshaft position sensor or any of the other errors I listed). But after driving it for about 3-4 miles of local traffic, less than 10 stop and go, the shifting problem will happen and all the error will show up again.

I am wondering if some how the transmission controller was having some problem, cause the rough shift, which makes the engine speed fluctuate from this abrupt load change introduced by the bad shift, causing the engine control computer to interpret it as a crankshaft sensor sending bad signal. This was the reason for my doubt the crankshaft sensor being bad. I should note the rough shift is very rough, it makes big jolt if someone hit me.