Is there a way to read JSON data inside Custom Fields without editing PHP? [closed]

Yes. Use JSON.parse($string); to convert your string value to JSON format within Javascript.

<script>
    var json_data_string = '{"data":["string no 1","string no 2","string no 3"]}'; // or echo the json_data field as <?php echo $json_data; ?>
    var json_data = JSON.parse(json_data_string);
    // Now access the properties as 
    $data = json_data.data; // outputs: string no 1,string no 2,string no 3
    $string1 = json_data.data[0]; // outputs: string no 1 
</script>

Reference to JSON.parse() function in Javascript.