Arduino first timer!! Why don`t this program work

  int Skallsikring1 = 2;
  int Skallsikring2 = 3;
  int Skallsikring3 = 4;
  int UtgangAlarm = 13;
  void setup() {
      Serial.begin(9600);
      pinMode(Skallsikring1, INPUT);
      pinMode(Skallsikring2, INPUT);

So SkallsikringX are Arduino pin numbers?

      if (Serial.available()) {
            if ((Skallsikring1 == HIGH) || (Skallsikring2 == HIGH)|| (Skallsikring3 == HIGH) == HIGH){
              digitalWrite(UtgangAlarm, HIGH);

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But here, you are accessing only the pin numbers; to test the values of the pins themselves, you need to access them via the digitalRead() function:

           if ((digitalRead(Skallsikring1) == HIGH) || (digitalRead(Skallsikring2) == HIGH) ...

Also, you check Serial.available(), but never actually read the data, so once you've sent data, Serial.available() will be true forever...