Without pressing the accelerator, the tachometer fluctuates up and down intermittently. When the RPM is high, the car shakes quite significantly. Is this normal?

Aren't you buying this car just for the same engine as the Honda Avancier 2.0T? The transmission is the same 8AT Aisin used by Toyota. Don't you trust Japanese brands?

My car was like this before, with white smoke coming out of the exhaust pipe. I had it towed to the 4S shop, and they said the fuel injector was clogged, so they replaced it with a new one.