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Formatting ISO time with Luxon

Using Luxon JS, I've been trying to format datetime to output in a certain format, using the native toISO function:
This is what I get:
"2018-08-25T09:00:40.000-04:00"
And this is what I want:
"2018-08-25T13:00:40.000Z"
I know that they are both equivalent in terms of unix time and mean the same thing except in a different format, I just want to be able to out the second string rather than the first. I looked through the Luxon docs but was unable to find any arguments/options that would give me what I need.

As other already stated in the comments, you can use 2 approaches:
Convert Luxon DateTime to UTC using toUTC:
"Set" the DateTime's zone to UTC. Returns a newly-constructed DateTime.
Use toISOString() method of JS Date.
You can use toJSDate() to get the Date object from a luxon DateTime:
Returns a JavaScript Date equivalent to this DateTime.
Examples:
const DateTime = luxon.DateTime;
const dt = DateTime.now();
console.log(dt.toISO())
console.log(dt.toUTC().toISO())
console.log(dt.toJSDate().toISOString())
console.log(new Date().toISOString())
<script src="https://cdn.jsdelivr.net/npm/luxon#1.26.0/build/global/luxon.js"></script>

From documentation I saw that in the method .fromISO of DateTime you can add an option object after the string of ISO date ("2018-08-25T09:00:40.000-04:00" in your example). In this object specify zone: utc like that:
const DateTime = luxon.DateTime;
const stringDate = "2018-08-25T09:00:40.000-04:00";
const dt = DateTime.fromISO(stringDate, {zone: 'utc'});
console.log('This is your date format', dt.toISO())
<script src="https://cdnjs.cloudflare.com/ajax/libs/luxon/1.26.0/luxon.min.js"></script>

How to format date with date-fns?

I've been trying to format a date using date-fns but I keep failing. Basically I have it working just fine with momentJS but not with date-fns:
Here's my date:
"10-13-20" // month, day, and year
Now with momentJS it works just fine like this:
let result = moment("10-13-20", 'MM-DD-YY').format()
// result = "2020-10-13T00:00:00-06:00"
So I'm trying to do the same using date-fns but no luck. Can anyone point me in the right direction? Thanks in advance!
let result = format(new Date("10-13-20"), 'MM-DD-YY') // Not working

As you can see, with moment lib, we need 2 steps to get the result: parse string to Date object, then format date object to string.
Your code - format(new Date("10-13-20"), 'MM-DD-YY') is format step, try convert a date object to a string with format template is MM-DD-YY. But your date object is not correct.
The solution is doing the same with moment lib:
Parse date string to date object. Use parse
const dateString = '10-13-20';
const date = parse(dateString, 'MM-dd-yy', new Date()) // not MM-DD-YY
Format date object to result string. Use format
const result = format(date, "yyyy-MM-dd'T'HH:mm:ss.SSSxxx")
console.log(result)
Result will be like (the same with moment's result in my timezone):
2020-10-13T00:00:00.000+09:00

const date = "2021-12-20"
console.log(format(parseISO(date), "dd-MM-yyyy"));
// output: 20-12-2021

How to convert into Date time

When the date is passed from my c# to JavaScript it returns the date time as {4/3/2020 12:00:00 AM}
but in JavaScript it is shown as 1585852200000.
What is the format that is being used? And how can i convert it back?

You need to convert the Unix timestamp to DateTime format,
var localDate = new Date(1585852200000).toLocaleDateString("en-US")
console.log(localDate); // only local date
var localTime = new Date(1585852200000).toLocaleTimeString("en-US")
console.log(localTime) // only local time
// local datetime
console.log(new Date(1585852200000).toLocaleString());

1585852200000 is epoch date.
you can convert it as
var date = new Date(1585852200000)
console.log(new Date(1585852200000));

As an alternative from Shivaji's answer:
When you are passing the date through to JS you could cast it as a string with DateTime.ToString("dd/MM/yyyy") seen here on MSDN.
This will keep its integrity visually, if it is just for display purposes, otherwise you will need to re-cast appropriately in JS (in which case use Shivaji's answer).

JavaScript Date's object will return the DATE object and it's POSITION that is being assigned in your computer. So, when you are working with a date or datetime types, you can use some of the methods that are provided by the Date object, such as getDate() and getDay(). But, a better solution would be to format the Date object itself. For example: use the toString() or toUTCString() methods.
var d = new Date();
document.getElementById("demo").innerHTML = d.toString();
Reference:
https://www.w3schools.com/js/js_date_formats.asp
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Date

Parsing Time Variabale

I have a time stamp that i'm using for the x-axis of my line charts, as of now i'm just passing it as "2018-11-29T20:32:24.025Z" I would like to clean this up to only display the day, hour, and minute. It looks like Moment.js is a popular library for this, but i'm having some problems formatting it.
Failed Attempt
let parsedDate = moment(parsedData.published_at,'DD--hh--mm')

You need to
Parse the date
let parsedDate = moment(parsedData.published_at);
Format the date
let formattedDate = parsedDate.format(...
See the documentation.

If I understand your question correctly then you can pass your inputDate (ie 2018-11-29T20:32:24.025Z) directly to the moment constructor.
Doing this will give you a moment object for that inputDate string, and from that you can call format() with your DD--hh--mm pattern to format the required string:
let inputDate = "2018-11-29T20:32:24.025Z";
// Create a moment object from input string
let parsedDate = moment(inputDate);
// Format a string from moment, based on the required pattern
let formattedData = parsedDate.format('DD--hh--mm');
console.log(formattedData);
<script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.22.2/moment.min.js"></script>

What is the right way to pass a date as a string in a specific format and return a date object with momentjs?

I have been looking at the momentjs momenjs documentation because I want to use it to return a date object from a date that is a string in a particular format. My code looks like this.
const date = moment(stringDate, 'YYYY-MM-DD HH:MM:SS');
console.log(date);
But it creates an invalid date as can be seen here.
What am I doing wrong. How can I get a date object from a date string that is in a particular format?

You're using MM:SS for minutes:seconds, but it should be mm:ss; details here.
Example:
const stringDate = "2018-05-11 14:25:37";
// Parsing
const m = moment(stringDate, 'YYYY-MM-DD HH:mm:ss');
// Show it in a different format to demonstrate parsing worked
console.log(m.format("DD/MM/YYYY HH:mm"));
// Accessing the underlying Date object
const dt = m.toDate();
// Log that dateobject
console.log(dt);
<script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.22.1/moment.min.js"></script>

In order to parse a string then return a different format you can:
> moment(dateString).format('DD.MM.YYYY')
Further examples:
Official docs: https://momentjs.com/docs/
Other sources: https://coderwall.com/p/vc3msa/a-very-short-introduction-to-moment-js