Undefined variable PHP POO

I'm just starting out in the PHP world, and I had a problem that I did not find a solution for, I looked everywhere and did not find something that could help me. My situation is as follows, I am working on a questionnaire and at the moment of instantiating the object the% Undefined variable error jumps. this is the object:

<?php
    class quiz {
      public $name;
      public $author;
      public $subject;
      public $questions = [];

      public function __construct($n,$a,$s){
        $this->name = $n;
        $this->author = $a;
        $this->subject =$s;
      }
      public function addq($q){
        $this->questions[] = new question($q);
      }
      public function getName(){
        echo  $this->name;
      }
    }
    class question {
     public $question;
     public $answers = [];

     public function __construct($q) {
       $this->question = $q;
     }

     public function adda($a, $v){
       $this->answers[] = new answer($a, $v);
     }

     public function getQuestion(){
       echo  $this->question;
     }
   }
   class answer {
     public $answer = [];

     public function __construct($a, $v) {
        $this->answer[] = array(
         'risposta' => $a,
         'valore' => $v,
        );
     }

      public function getAnswer(){
        //codificazione in json per una lettura più efficace
        $tmp = json_encode(array_column($this->answer, 'risposta'), TRUE);
        //sotto stringa per prendere unicamente il valore della risposta senza [""] inserito da json
        $tmp = substr($tmp,2,strlen($tmp)-4);
        //stampa della variabile preparata in precedenza
         print_r($tmp);
      }
   }
?>

and instantiate the object quiz aca:

   <?php
      session_start();

     //reindirizzamento
     $urlRedirect = 'http://localhost:8888/prova%20ogetti/view/aggiungidomanda.php';
     header('Location:'.$urlRedirect);

     //autoload di classi esistenti all'interno del progetto
     function __autoload($classname) {
        $filename = "../model/". $classname .".php";
        include_once($filename);
     }

     //presa de  dati inviati tramite post
     $name = $_POST['nome'];
     $author = $_POST['autore'];
     $subject = $_POST['materia'];
     //$image = $_POST['file'];

     //creazione del ogetto quiz
     $obj = new quiz($name, $author, $subject);

     //inizializzazione delle variabili di sessione
     $_SESSION['obj'] = serialize($obj);
     $_SESSION['state'] = "q";
     session_write_close();
  ?>

The problem arises when I try to add the question with the respective answers in another file:

   <?php
     session_start();
    //iniziamo la sessione
    //reindirizzamento automatico
     $urlRedirect = 'http://localhost:8888/prova%20ogetti/view/aggiungidomanda.php';
    //header('Location:'.$urlRedirect);

    include("../model/quiz.php");


    //prendiamo l'ogetto "quiz" creato in precedenza dalla variabile di sessione
    $obj = unserialize($_SESSION['obj']);

    // prendiamo le variabile passate tramite post dalla vista aggiungidomanda
    $domanda = $_POST['domanda'];
    $risp1 = $_POST['risp1'];
    if($_POST['val1'] = null){$val1 = "false";}else{$val1 = "true";};
    $risp2 = $_POST['risp2'];
    if($_POST['val2'] = null){ $val2 = "false";}else{$val2 = "true";};
    $risp3 = $_POST['risp3'];
    if($_POST['val3'] = null){ $val3 = "false";}else{$val3 = "true";};
    $risp4 = $_POST['risp4'];
    if($_POST['val4'] = null){ $val4 = "false";}else{$val4 = "true";};

    $obj->addq($domanda);

    //aggiungo la risposta e il valore corrispondente nella domanda rispettiva
    $obj->$questions[count($obj->$questions)-1]->adda($risp1,$val1);
    $obj->$questions[count($obj->$questions)-1]->adda($risp2,$val2);
    $obj->$questions[count($obj->$questions)-1]->adda($risp3,$val3);
    $obj->$questions[count($obj->$questions)-1]->adda($risp4,$val4);

    session_write_close();
  ?>

the error that comes out would be this: Undefined variable: questions in ... on line 34 What am I doing wrong?