[Quiz game] How do I make players contribute with questions?

I would do it like this:

Crate a new class "Question":

 using UnityEngine;
 using System.Collections;
 using System.Collections.Generic;
 
 [System.Serializable]
 public class Question {
 
     public string questionText = "What currency does the United States use as of 2015?";
         public List<string> answers = new List<string>() {"Dollar", "U.S. Dollar", "USD", "US Dollar"};
 
 
 }

I use a list for the answer string so more than one answer can be correct if I wish.

Then, create a questionaire: Simply a list of the Question class:

 public List<Question> questionaire = new List<Question>();

Now you can let players Add questions simply by adding to the list and filling in the values for questionText and answers.

To draw a random question:

 string newQuestion = questionaire[Random.Range(0, questionaire.Count - 1)];
 
 string questionTextCur = newQuestion.questionText;
 
 

To check if an answer is correct:

 string answerText = "Euro";
 
 if(newQuestion.answers.Contains(answerText)) {
      Debug.Log("Right answer!");
 }
 else {
      Debug.Log("Wrong answer!");
 }

If by storing and retrieving you mean actually saving and loading to/from file, then look into Serialization and BinaryFormatters.