How does the microprocessor convert the machine code to micro code? What part of the processor is at play?
The Control Unit converts machine instructions into micro-code.
There are two types of control units; Micro-programmed & Hardwired. Both work differently.
In micro-programmed control the control unit is an interpreter for the individual machine instructions. It runs in a loop interpreting instruction after instruction, generating the required micro-instructions and control & timing signals.
In hardwired control the control unit is a state machine which takes logic signals from the instruction and generates various control signals which run the hardware.