With EcmaScript 6 (ES2105), creating an array containing five nulls is as easy as this:

const arr = new Array(5).fill(null);

MDN Reference

Given that there are only 2 potential values for each item in the 2D array, you will avoid allocating extra memory if you actually don't initialize the whole 2D array since JS arrays are essentially hashes (good explanation here: https://stackoverflow.com/a/20323491/2611078).

Initialize array:

var arr = [];

Then, when updating an item after user action:

 if (!arr[i]) { 
     arr[i] = [];
 }
 arr[i][j] = true;

Then, when checking the array:

if (arr[i] && arr[i][j]) {
    console.log('value');
} else {
    console.log('other (default) value');
}

A side note: Your solution doesn't actually check for an all-null array. It just checks for an all-falsey array. [0, false, ''] would still pass the check.

You could use the Array#every method to check that every element of an array meets a certain condition:

const arr = [null, null, null];
console.log(arr.every(element => element === null));

every takes a callback in which the first argument is the current element being iterated over. The callback returns true if the element is null, and false if it is not. If, for all the elements, the callback returns true, it will evaluate to true, thus if all elements in the array are null, it's true.

Use some which returns a boolean:

const arr = [null, 2, null, null];
const arr2 = [null, null, null, null];

function otherThanNull(arr) {
  return arr.some(el => el !== null);
}

console.log(otherThanNull(arr));
console.log(otherThanNull(arr2));

If you have a DOM node in an array in javascript and then remove it from the DOM (e.g. after your ajax call), the node will continue to exist in the array, and continue to take up space. You can then add it to the DOM again later if you wish.

If you do not add it to the DOM again, and instead set the item in the array to some other value such as null or undefined, assuming that there are no remaining references to that element, it will be garbage collected and no longer take up space.

It's worth bearing in mind that there is a difference between a javascript array and a NodeList or a HTMLCollection. You can get a node list by calling some DOM methods such as document.getElementsByTagName. NodeLists look a bit like arrays, but remain 'live', so if a node is removed from the DOM it will be removed from the NodeList too.

I would make it way more simpler without the counter. You have the total in the length of the array.

I also added a version using array.reduce().

And please, don't use numbers variable inside the function. It makes no sense here. You pass the variable to the function and inside the function you should use the received variable or it will behave incorrectly. Inside the function numbers is called "arr", so use arr all the way.

function average(arr){
    if (arr.length === 0) return null;

    let total = 0;
    arr.forEach(function(item){
        total += item;
    })
    return total / arr.length;
}

// using array.reduce() which makes more sense here
function average2(arr){
    if (arr.length === 0) return null;

    const total = arr.reduce(function(prev,next){
      return prev + next;
    });
    return total / arr.length;
}

console.log(average([]));
console.log(average([1,2,3]));

console.log(average2([]));
console.log(average2([1,2,3]));