The Engine Check Light is showing on the dashboard

What is your question?

I bought it as a second hand car dealers in Japan. The car dealer told me the O2 need to be changed. The day it was serviced by Mazda Amtec, the check light disappears. But after driving for less than a kilometer it reappears again. The car perfomance is so good as I was driving it for almost three months. I sent it back to Amtec Mazda and they told me to change the oxygen sensors, the catalytic converter must be changed as well. So Im now confused. So what is the real problem now. There are no codes shown on the dashboard. I just noticed in the morning when you start it produces a white smoke from the exhaust pipe and it disappears after some few minutes when the engine is running.