Here is some edit in your code

#include <SoftwareSerial.h>
#include<Arduino.h>

//Arduino Micro
//SIM 800l


SoftwareSerial mySerial(9,10); // RX, TX 

void setup()  
{
  // Open serial communication
  Serial.begin(9600);

  // set the data rate for the SoftwareSerial port
  mySerial.begin(9600);

  Serial.println("Setup finished");

}

void loop() // run over and over
{
  Serial.println("Sending AT command");
  mySerial.write("AT"); //OK should be returned
  delay(1000);
  //read sim-module response
  Serial.println("Response: ");
  while( mySerial.available() )
  {
    String c = mySerial.readString();
    Serial.println(c);
  }

  mySerial.write("at+cmee=2"); //set sim-module into debug mode

  delay(1000);

  mySerial.write("at+cpin?"); //check if pin is necessary


  //read sim-module response
  while( mySerial.available() )
  {
    String c = mySerial.readString();
    Serial.println(c);
  }

}

Change UART pins to 9,10 as 0,1 are already used in normal serial. Secondly change Seria.read() to Serial.readString() because as far as i know the response is string.

Here is some edit in your code

#include <SoftwareSerial.h>
#include<Arduino.h>

//Arduino Micro
//SIM 800l


SoftwareSerial mySerial(9,10); // RX, TX 

void setup()  
{
  // Open serial communication
  Serial.begin(9600);

  // set the data rate for the SoftwareSerial port
  mySerial.begin(9600);

  Serial.println("Setup finished");

}

void loop() // run over and over
{
  Serial.println("Sending AT command");
  mySerial.write("AT\r\n"); //OK should be returned
  delay(1000);
  //read sim-module response
  Serial.println("Response: ");
  while( mySerial.available() )
  {
    String c = mySerial.readString();
    Serial.println(c);
  }

  mySerial.write("at+cmee=2\r\n"); //set sim-module into debug mode

  delay(1000);

  mySerial.write("at+cpin?\r\n"); //check if pin is necessary


  //read sim-module response
  while( mySerial.available() )
  {
    String c = mySerial.readString();
    Serial.println(c);
  }

}

Change UART pins to 9,10 as 0,1 are already used in normal serial. Secondly change Seria.read() to Serial.readString() because as far as i know the response is string.