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Why new Date() with `T17:00:00.000Z` is returning the next date?

When I try this new Date('2015-01-25T17:00:00.000Z') it will returning the next date Jan 26 2015 00:00:00, this is an expected behaviour for me, but why it is like this?
Is there any explanation from this js behaviour when using TZ with value of OO:OO:OO.

The Z at the very end means "Zulu Time" which is another word for UTC.
The result you see in your console is the time in your current timezone. You are probably 5 hours ahead of UTC.
If you remove the Z, the output you get is the same as what you put in, because Javascript will use local time by default.

UTC (Zulu) time is '2015-01-25T17:00:00.000Z'. The local time in Jakarta is UTC+7: Jan 26 2015 00:00:00.
See Time in Indonesia and ISO 8601.

Javascript Date, setFullYear changes timezone

Javascript Dates work with timezones. If I create a date, it sets the timezone. When I update the year of that date, I don't expect the timezone to change. It does, however. The worst thing is that it changes the timezone but not the time, causing the actual time to shift by one hour!
This causes the issue that if I have the person's birth date, and want to know his birthday this year, I cannot simply set the year to the current year using birthdate.setFullYear(2018), because it will return the birthday minus one hour. That means that it occurs one day before the actual birthday, at eleven 'o clock.
let test = new Date('1990-10-20');
console.log(test);
console.log(test.toISOString().substring(0, 10));
// 1990-10-20 ( Sat Oct 20 1990 01:00:00 GMT+0100 (Central European Standard Time) )
test.setFullYear(2000);
console.log(test);
console.log(test.toISOString().substring(0, 10));
// 2000-10-19 ( Fri Oct 20 2000 01:00:00 GMT+0200 (Central European Summer Time) === one hour too soon!! )
It might be that your timezone does not reproduce, here is my output:
"1990-10-20T00:00:00.000Z"
1990-10-20
"2000-10-19T23:00:00.000Z"
2000-10-19
The only workaround I found is substring the date and replace it as string values. How can I do it better using the Date object?

Hm, maybe it would be better to use setUTCFullYear(...) (MDN Docs) instead? At least in that case, it won't mess up the time.
let test = new Date('1990-10-20');
console.log(test);
console.log(test.toISOString().substring(0, 10));
// "1990-10-20T00:00:00.000Z")
test.setUTCFullYear(2000);
console.log(test);
console.log(test.toISOString().substring(0, 10));
// "2000-10-20T00:00:00.000Z"

BEWARE THE TIMEZONE If you want to work with just-a-date using the date object (and you more or less have to) your date objects should represent UTC midnight at the start of the date in question. In your case, to indicate a year, use UTC midnight at the start of the 1st January. This is a common and necessary convention, but it requires a lot of attention to make sure that the timezone doesn't creep back in, as you've discovered.
When you say "javascript dates work with timezones", a javascript date is a moment in time (ticks since the epoch) with handy static functions for converting that moment into a meaningful string in the local timezone (or a specified timezone). The date object itself does not have a timezone property.
So, you can create your UTC midnight year with something like...
var myDate = new Date(Date.UTC(2018,0,1)); // months are zero-indexed !
Then serialize it specifying UTC...
myDate.toISOString();
myDate.toLocaleDateString("en",{timezone:"UTC"});

.NET date, Moment.js, UTC and Timezone shifting

I've got a UTC date through an Ajax call, e.g. "/Date(1517216466000+0100)/",
which is when printing to the console: Mon Jan 29 2018 10:01:06 GMT+0100 (W. Europe Standard Time).
What I need to do, is to let the user change the timezones: I can easily do it with e.g. moment(myDate).tz("Japan").
Then I need to save the date in it's UTC format, which I am not able to do.
I've been experimenting with moment.utc(), but for the input above, it returns 1 hour less.
How to deal with this situation? In summary:
1. Get a UTC time from a webservice
2. Let the user change the timezones
3. Save the modified date in UTC (without the timezone)
Working demo: https://stackblitz.com/edit/angular-kqrct7?file=app%2Fapp.component.html
EDIT for clarification:
Let's just have a look at the hours. What I get the date from the WCF, is 10 o'clock. The browser interprets it as 10 o'clock BUT in GMT+1 so when I convert it to UTC, it becomes 9 o'clock.
I want it to be 10 o'clock as UTC. Then, if I modify the timezone and e.g. the minutes of this date, I want to be able to get the UTC value of this date.
EDIT2: Made my question simplier for clarification
I've got a UTC date, which I get from a webservice like: "/Date(1517216466000+0100)/" which is: Mon Jan 29 2018 10:01:06 GMT+0100 (W. Europe Standard Time) when printed to console.
I add a timezone to it with moment(this.inputDate).tz("Europe/Berlin").format(), but it stays 10:01:06, I guess because of my browsers GMT+1.
I want the ORIGINAL string to be used as a UTC date AND it should remain 10:01:06, not 09:01:06 as you can see above (2nd moment example), so with the timezone "Europe/Berlin" would be 11:01:6

In the .NET JSON formatted date "/Date(1517216466000+0100)/" the timezone offset can be ignored. It represents "2018-01-29T09:01:06.000Z", where the source system was at a timezone offset of +0100. So if you don't care about the source timezone, just ignore it.
It is also an identical moment in time to Mon Jan 29 2018 10:01:06 GMT+0100 (W. Europe Standard Time), just with a different offset.
UTC is not a format, it's a time standard. If you want to use ISO 8601 format:
Extract the first numeric value
Convert to Number
Pass to the Date constructor
Call the toISOString method on the resulting Date
var s = '/Date(-1517216466000+0100)/';
console.log(new Date(+s.replace(/^[^\d-]+(-?\d+).*$/,'$1')).toISOString());
You can also parse and format it using moment.js, which according to the documentation can handle the .NET JSON format without needing to specify the format. So you can either do that or extract the time value and parse it with the "x" format token:
var s = '/Date(1517216466000+0100)/';
// Let moment.js guess the format
console.log(moment(s).utc());
// Extract time value and supply format
console.log(moment(s.replace(/^[^\d-]+(-?\d+).*$/,'$1'), 'x').utc());
<script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.20.1/moment.min.js"></script>

"/Date(1517216466000+0100)/" is a non-standard way to serialise a date/time. Take a look at ISO8601 which defines several standard ways to represent dates and times.
That being said let's take a look at what this gets evaluated as...
moment("/Date(1517216466000+0100)/").toDate()
gives Mon Jan 29 2018 09:01:06 GMT+0000 (GMT Standard Time) for me (in the UK)
taking just the timestamp value 1517216466000
new Date(1517216466000)
also gives Mon Jan 29 2018 09:01:06 GMT+0000 (GMT Standard Time)
this means that the +0100 is being ignored.
You're not actually modifying the time so why would you expect it to save back as anything other than Mon Jan 29 2018 09:01:06
UPDATE
But the "original" string represents Mon Jan 29 2018 09:01:06 UTC the +0100 is ignored and it's just coincidence that your offset to UTC is also +0100. An off.
Offset and timezone are 2 different things. A timezone encompasses offset to UTC as well as when/if daylight savings comes in to force. Just because it says +0100 doesn't necessarily mean (W. Europe Standard Time) as it could just as easily be (West Africa Time) which is also UTC+0100 but doesn't observe daylight savings at all.
The time you have "/Date(1517216466000+0100)/" doesn't convey enough information to say which timezone it is and JS/moment just uses the timestamp 1517216466000 and as such uses UTC. When you console.log() this the browser writes it to screen as local time Mon Jan 29 2018 10:01:06 GMT+0100 (W. Europe Standard Time) but this is only a representation of the underlying datetime.
By telling moment to use a specific time zone, it's only changing how the date/time gets displayed and doesn't actually change the time it represents.
If you use a date picker to change the date/time then you'll have to serialise the value to send to the backend in an appropriate way that the .Net app you cannot change will understand and conveys what you intend.
Example
Get date from server as var serverTime = "/Date(1517216466000+0100)/"
convert this to a JS Date using moment var time = new moment(serverTime)
Let user specify TimeZone i.e. Japan Standard Time (UTC+9) time = time.tz("Japan")
time still represents Mon Jan 29 2018 09:01:06 UTC but when displayed on screen with time.format() gives "2018-01-29T18:01:06+09:00"
You stated "I want it to be 10 o'clock as UTC". Unfortunately the value you've is NOT 10 O'clock UTC and will never be 10 O'clock UTC because it isn't. It is 9 O'clock UTC
You could parse the value you get from the server yourself but the time from the server IS 9am UTC. If you change it to 10 am UTC then you would see that as Mon Jan 29 2018 11:01:06 GMT+0100 (W. Europe Standard Time) - 11 O'clock local time.

Thanks everyone for your detailed answers, they helped me a lot in understanding my problem! However, the right solution was the following:
10 o'clock was a UTC time in the database and it got interpreted as 9 o'clock UTC in Moment.js because C# handled it as a local time. So, before sending the date to the client, I had to indicate that its a UTC:
var utcToClient = DateTime.SpecifyKind(downtime.DownTimeStartUTC, DateTimeKind.Utc)
Then, in Moment I could create a UTC with:
var jsUtc = moment.utc(downtime.DownTimeStartUTC)
Changing the timezones was a breeze with:
jsUtc.tz(userSelectedTimezone)
And saving the date in the database, I used this in C#:
var utcFromClient = Record.DownTimeStartUTC.ToUniversalTime()

Javascript new Date decreases date by a day

I have a scenario where I am using AngularJS to read date. Interestingly it decreases my date value by one.
Why is this happening?
new Date("2016-01-06T00:00:00")
give me result as
Tue Jan 05 2016 16:00:00 GMT-0800 (Pacific Standard Time)

This is because when you use the new Date() in the JavaScript, it converts and prints the date in browsers timezone.
So if you print:
new Date("2016-01-06T00:00:00-0800")
You will get the actual output you want, because of the -0800 difference between your time zone (determined by the browser) and the UTC time.

The UTC time zone is used to interpret arguments in ISO 8601 format that do not contain time zone information (note that ECMAScript 2015 specifies that date time strings without a time zone are to be treated as local, not UTC).
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Date/parse
Since your date string appears to lack one, JS assumed it's UTC time. The result you see is the same moment in time, offset to your timezone. All you need to do is provide timezone data to the string you're parsing.

It is because the date is taking your browser's timezone in to account, which in your case is in PST. It does the same to me, in EST:
test = new Date("2016-01-06T00:00:00")
Tue Jan 05 2016 19:00:00 GMT-0500 (EST)
You can still obtain the time in UTC by using any of the .getUTC* functions, like so:
test.getUTCDate();
6

Unix epoch time: Adding days

In Javascript, I needed to add one single day to unix epoch timestamp. So, I tried adding 24*60*60*1000 or 86400000 milliseconds to my date, say: 1396306800000, which, as per http://www.epochconverter.com/ is: 4/1/2014 12:00:00 AM GMT+1. Now, when I try and add one day to it, to get the result, 1396393200000 which is: 4/2/2014 12:00:00 AM GMT+1.
Just one day, right?
Now, I try and subtract a day from the original 1396306800000 to get 1396220400000 or 3/31/2014 12:00:00 AM GMT+1
So far, so good.
Now, If I do one more subtraction, I get this: 1396134000000 which is 3/29/2014 11:00:00 PM GMT+0
How, is this possible? Subsequent subtractions are going smoothly with the same offsets. But at this particular point, 30th March is skipped entirely. Can anyone tell me whats going on?

Daylight savings time. Probably British Summer Time.
You've probably overlooked the GMT+1 in
3/31/2014 12:00:00 AM GMT+1
If you look at the earlier date, it's GMT+0:
3/29/2014 11:00:00 PM GMT+0
The United Kingdom (and other countries) switch time zones on the last sunday of March, which was March 30th this year (2014). The website uses your local time zone settings. This explains the apparent difference of one hour.

It is not skipping a day, you are not accounting for the daylight saving time.
During daylight saving adjustment the day is only 23 hours, which you are subtracting 24hrs from.

I was looking at the link you provided and also calculated and it's giving the correct result.
So if you subtract one day from 1396306800000 so it becomes 1396220400000=1396306800000-86400000
and the output is
GMT: Sun, 30 Mar 2014 23:00:00 GMT