Why the car has difficulty in fast acceleration

Hello, Before your check engine light comes on, and before the problem gets any worse, have your high pressure fuel pump (mechanical fuel pump) checked. Some of the older TDI engines suffered from premature failure of the high pressure fuel pump, and this causes system wide damage, and repair involves replacing the entire fuel system. I'm not saying that you certainly have this issue, but the noise and loss of power you are describing is consistent.