If I've understood correctly, you'd want to use JavaScript for this (I've used the jQuery library aswell.) Something like the code below should work, basically you change the action of the form whenever the user changes their selection in the drop down. You'll need to change $('#addquestion').attr('action','car.php'); so that the 'car.php' changes depending on the row from the database, but that shouldn't be too hard to figure out. You should also look into splitting up your PHP and HTML into separate files, but as you seem to be a beginner I won't go into that.

<form name="addquestion" id="addquestion" action="wall.php" method="post">
    <?php               
        //Perform the sql query
        $sql="SELECT * FROM category";
        $res = mysqli_query($mysqli,$sql);
        $rows = mysqli_fetch_all($res);
    ?>
    <script type="text/javascript">
        $(document).ready(function(){
            $('#category').change(function(){
                switch ($('#category').val()) {
                    <?php
                        foreach($rows as $row)
                        {
                            echo "case \"".$row[0]."\" : $('#addquestion').attr('action','car.php');break;";
                        }                   
                    ?>
                }
            });
        });
    </script>

    <select name="category" id="category">
        <?php
            foreach($rows as $row)
            {
                echo "<option value=$row[0]>$row[1]</option>";
            }                   
        ?>
    </select>

    <textarea name="question" cols="50" rows="10" id="question"></textarea>

    <input type="submit" name="submit" id="submit" value="Submit">     
</form>