Problems loading from file to arraylist

Some issues:

Your List<String> question = new ArrayList<String>(); should instead be something like List<Question> questionBank = new ArrayList<Question>(); since holding everything as a string (instead of a Question object) would be significantly messier. The name questionBank is also more descriptive than question when reading the code. I would also recommend having the questionBank as a class variable so it's easily accessible throughout your Quiz class.

You never add the questions to your ArrayList but I suspect you already know that and it was just low priority while fixing the other issues.

Your Question class is also a bit unconventional. A better way to structure it might be something like this:

public class Question {

     private int correctAnswer;
     private int numOfTries;
     private int numOfCorrectTries;
     private String question;
     private String[] answerChoices;

     public Question(String question, String[] answerChoices,
             int correctAnswer, int numOfTries, int numOfCorrectTries) {
         this.question = question;
         this.answerChoices = answerChoices;
         this.correctAnswer = correctAnswer;
         this.numOfTries = numOfTries;
         this.numOfCorrectTries = numOfCorrectTries;
     }

     public void getQuestion() {
            System.out.println("Question: " + question);
            System.out.println("Answer: ");
            for (int i = 0; i < answerChoices.length; i++) {
                System.out.println(answerChoices[i]);
            }
     }

     public double getPercentageRight() {
         double percentageRight = (numOfCorrectTries / numOfTries) * 100;
         percentageRight = Math.round(percentageRight * 100);
         percentageRight = percentageRight / 100;
         return percentageRight;
     }

}

I removed the variable for numberOfChoices since that is the same as answerChoices.length. I also renamed your Question to question since variables in Java usually follow camelCase. I'm not sure what the other methods are for or how they should display output so I mostly left them alone.

For reading to a file I think you can do something similar to what you have, but I'll post the code I have that conforms to the new constructor for the Question class.

private void addQuestions() {
    File quizText = new File("quiz.txt");
    try {
        Scanner fileIn = new Scanner(quizText);
        while (fileIn.hasNextLine()) {
            String question = fileIn.nextLine();
            int numberOfAnswers = fileIn.nextInt();
            fileIn.nextLine();
            String[] answers = new String[numberOfAnswers];
            for (int i = 0; i < numberOfAnswers; i++) {
                answers[i] = fileIn.nextLine();
            }
            int correctAnswer = fileIn.nextInt();
            int numOfTries = fileIn.nextInt();
            int numOfCorrectTries = fileIn.nextInt();
            fileIn.nextLine();
            Question nextQuestion =
                new Question(question, answers, correctAnswer, numOfTries, numOfCorrectTries);
            questionBank.add(nextQuestion);
        }
        fileIn.close();
    } catch (IOException e){
        e.printStackTrace();
        System.out.println("File Not Found.");
        return;
    }
}

I also made the variables private but you can create a custom getter for them to prevent them from being directly accessed (and/or changed) from the outside. Using this code I was able to create a question bank with all five questions and display the correct answer along with all possible choices so hopefully it points you in the right direction.

I re-did you quiz class. In my example all your questions stated above is answered. I'll explain them one by one.

public class Quiz {

List<Question> question = new ArrayList<Question>();

public void writeFile() {
    Question qn = new Question();
    try {
        PrintWriter out = new PrintWriter("quiz.txt");
        out.println(qn.Question);
        out.println(qn.numberOfChoices);
        qn.answerChoices = new String[qn.numberOfChoices];
        for (int i = 0; i < qn.numberOfChoices; i++) {
            out.println(qn.answerChoices[i]);
        }
        out.println(qn.correctAnswer);
        out.println(qn.numOfTries);
        out.println(qn.numOfCorrectTries);
        out.close();
    } catch (IOException f) {
        System.out.println("Error.");
    }
    qn.getQuestion();
}

public void readFile() {
    File file = new File("quiz.txt");
    boolean exists = file.exists();
    Quiz q = new Quiz();
    Question a = new Question();
    String[] answerChoices;
    try {
        if (exists == true) {
            Scanner s = new Scanner(file);
            String line = "";
            while (s.hasNextLine()) {
                line = s.nextLine();
                if (line.startsWith("---")) {
                    a = new Question();
                    a.Question = line.substring(4);
                } else if (line.startsWith("choices : ")) {
                    a.numberOfChoices = Integer.parseInt(line.substring(10).trim());
                    a.answerChoices = new String[a.numberOfChoices];
                    for (int i = 0; i < a.numberOfChoices; i++) {
                        a.answerChoices[i] = s.nextLine();
                    }
                } else if (line.startsWith("correct answer : ")) {
                    a.correctAnswer = Integer.parseInt(line.substring(17).trim());

                } else if (line.startsWith("No of Tries : ")) {
                    a.numOfTries = Integer.parseInt(line.substring(14).trim());

                } else if (line.startsWith("No of correct Tries : ")) {
                    a.numOfCorrectTries = Integer.parseInt(line.substring(22).trim());
                    question.add(a);
                }
            }
        } else {
            q.writeFile();
        }
    } catch (IOException e) {
        System.out.println("File not found.");
    }
}

public static void main(String[] args) {
    Quiz qz = new Quiz();
    qz.readFile();
    Question b = new Question();
    int selection;

    //real program starts here
    System.out.println("Welcome to the Quiz Program! Good luck!");
    System.out.println("****************************************");

    b = qz.question.get(2); // you can implement how your questions are taken from list of questions
    b.getQuestion();
    Scanner in = new Scanner(System.in);
    System.out.print("Your answer?: ");
    selection = in.nextInt();

    if (selection == b.correctAnswer) {
        b.numOfCorrectTries++;
        System.out.println("Correct answer");

    } else {
        System.out.println("Incorrect answer");
    }
}

}

1) loading quiz question from file and storing in arraylist and accessing it (need help!)

Instead of using

 List<String> question = new ArrayList<String>();

use below as class variable. So you can access them anywhere inside your class

 List<Question> question = new ArrayList<Question>(); 

2) correct answer not accepted - gives me error (logic error)

Logic is corrected in the main block.

3) not all answer choices are displayed

Re-did you readFile() method. but to be success with this logic you need to recreate your quiz.txt as below.

--- How many licks does it take to get to the tootsie roll center of a tootsie pop?
choices : 4
one
two
three
four
correct answer : 2
No of Tries : 14
No of correct Tries : 5
--- What is your name?
choices : 3
Arthur, King of the Britons
Sir Lancelot the Brave
Sir Robin the Not-Quite-So-Brave-As-Sir Lancelot
correct answer : 0
No of Tries : 14
No of correct Tries : 6
--- Who's on first?
choices : 5
What
Why
Because
Who
I don't know
correct answer :  3
No of Tries : 14
No of correct Tries : 7
--- Which of the following is a terror of the fire swamp?
choices : 4
Lightning sand
Flame spurt
R.O.U.S.
All of the above
correct answer : 3
No of Tries : 14
No of correct Tries : 4
--- Who is the all-time greatest pilot?
choices : 6
Manfred von Richthofen
Chuck Yeager
Hiraku Sulu
Luke Skywalker
Kara Thrace
Charles Lindbergh
correct answer : 4
No of Tries : 14
No of correct Tries : 9

Note : Selection of the question is based on

   b = qz.question.get(2);

in the main(). To create a question paper based on randomly selected questions, you might create a separate method and prompt questions from this method. Refer Math.random() further.

Also better to create an XML file instead of txt for this kind of applications. Google for "Java and XML"

Hope this helps.