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Best way to detect browser window changes like go back, url change, reload, close event

So I am working on a testing application and I need to call a finsihTheTest() function (i.e. this function finishes the test by saving answers, time and other information) whenever following conditions occur:
User tries to reload page.
User tries to go back from the page.
User tries to close the tab.
User tries to close the browser window.
User goes to another url.
If anything happens that closes the page like laptop/PC shutdown, internet lost or anything else.
What I exactly want to do is, if once a user starts the test and by any mean he attempts to leave I want to save his state. Which is being done by the function finishTheTest().
I got a clue but it didn't work:
function UnLoadWindow() {
return 'We strongly recommends NOT closing this window yet.'
}
window.onbeforeunload = UnLoadWindow;

To get the full results for your cases there's many things you should now on how browsers react on many scenarios.
To understand more please read this section :
Especially on mobile, the unload event is not reliably fired. For example, the unload event is not fired at all in the following scenario:
A mobile user visits your page.
The user then switches to a different app.
Later, the user closes the browser from the app manager.
Also, the unload event is not compatible with the back/forward cache (bfcache), because many pages using this event assume that the page will not continue to exist after the event is fired. To combat this, some browsers (such as Firefox) will not place pages in the bfcache if they have unload listeners, and this is bad for performance. Others, such as Chrome, will not fire the unload when a user navigates away.
If you're specifically trying to detect page unload events, it's best to listen for the pagehide event.
window.addEventListener('pagehide', function(event) {
document.cookie = "saveData=test"
},false)
This way you can save your user current data and reload it on next page window load event

Chrome popstate not firing on Back Button if no user interaction

I'm trying to use "pushState" and the "popstate" event to trap Back button navigation, however, while the popstate event triggers correctly in Firefox, it doesn't trigger in Chrome (Version 76.0.3809.87 (Official Build) (64-bit)) if there is no user interaction.
From testing, it looks like the popstate event only gets triggered if the user interacts with the page (ie. clicks somewhere on the document). So if you load the page without interacting and hit Back, the popstate function is not called.
I've added a Fiddle to showcase this: https://jsfiddle.net/0xwvLndu/
To test the Fiddle in Chrome, just click the link and hit the Back button. You'll see no alert. Then click the link again but this time click anywhere on the Fiddle document and then hit the Back button, the alert is then triggered.
I found a discussion on the Chromium forum that may relate to this quirk, and perhaps this has been implemented to prevent abuse of history entries - https://groups.google.com/a/chromium.org/forum/#!topic/blink-dev/OCS7g72HtyI and https://github.com/WICG/interventions/issues/21#issuecomment-425609246
If this is the case, does it mean that popstate cannot be relied on anymore to trap Back button actions, and if so, is there a work around solution?
Below is an example of what I've been testing with:
window.addEventListener('load', function() {
history.pushState(null, null, document.URL);
});
window.addEventListener('popstate', function(event) {
alert('test');
});
I expected the alert to be triggered on Back Button regardless of user interaction, but this does not happen in Chrome.

Try adding a setTimeout of 0
window.onpopstate = () => setTimeout(alert.bind(window, "Pop"), 0);
When writing functions that process popstate event it is important to take into account that properties like window.location will already reflect the state change (if it affected the current URL), but document might still not. If the goal is to catch the moment when the new document state is already fully in place, a zero-delay setTimeout() method call should be used to effectively put its inner callback function that does the processing at the end of the browser event loop: window.onpopstate = () => setTimeout(doSomeThing, 0);
Content is taken from
https://developer.mozilla.org/en-US/docs/Web/API/Window/popstate_event
On a sidenote it is advised not to use this as browsers may remove this any time.

As others suggested in comment, this should be by design of browser software to prevent hijacking of its default back button behavior.

Vaadin onbeforeunload event

Is there any Out Of the Box Vaadin 10 (and higher) event similar to window.onbeforeunload in JavaScript?
I've tried to use onDetach() or beforeLeave(), but it only works inside UI, and when user reloads the page or closes the page it's not working.

You can use the approach described in https://vaadin.com/forum/thread/17523194/unsaved-changes-detect-page-exit-or-reload that was already suggested in a comment.
At the same time, I'd urge you to be really careful with beforeunload events since they are in some situations fired even though the user is actually not navigating away from the page.
The most common case is if the user clicks a link that starts a download. In that case the browser will fire the event immediately when the user clicks the link. Slightly later when the browser receives the response headers, it will discover that it's a download and not a new HTML page to display. The end result is then that beforeunload has been fired but the previous page is still kept running.
If you want to use the event for cleanup, then the best approach today is probably a combination of the unload event and then using the new-ish Beacon API for notifying the server that the user has actually navigated away. Integrating this into a Vaadin application will require slightly more JavaScript, but it has the benefit that it will actually work.

Javascript event that runs before page changes

Is there such a thing?
I know that I can hook my function on the click event of all links, but there are other situations where a page is changed, like refresh or when a different script changes the window.location
In the end, I did it by sending a string trough postMessage from the unload event, like this:
$(window).bind('unload', function(e){
window.parent.postMessage('unloading');
});
in the parent document:
$(window).bind('message', function(e){
if(e.originalEvent.data == 'unloading'){
// ajax stuff here
}
});
It appears to work.
I probably should have mentioned that there's a iframe involved :)

There's the beforeunload event, which is fired when the page is being torn down (either to follow a link, or if the window is being closed, or refresh, etc.). Example:
window.onbeforeunload = function(event) {
var s = "You have unsaved changes. Really leave?";
event = event || window.event;
if (event) {
// This is for IE
event.returnValue = s;
}
// This is for all other browsers
return s;
}
There are, for obvious reasons, very strict limits on what you can do in the handler of the beforeunload event, and as you can see above beforeunload handlers have a different signature than normal event handlers. Basically, your code can't do anything asynchronous, can't open new windows, and can't cancel the event. It can return a string, and if it does, the browser will pop up a window asking whether you really want to leave the page, and including your string in that pop-up.
From your comment on the question:
I need it before so I can fire a ajax request and update some things...
The way to do that here many years after the question was originally asked is with the beacon API. This lets you send a non-blocking asynchronous request to the server without slowing down the process of the browser tearing down your page and navigating to the next:
navigator.sendBeacon("/path/to/notify", optionalData);
It's a send-and-forget, but the browser doesn't cancel it when your page is torn down (like it does a standard asynchronous ajax request). Instead, it allows that request to complete even though your page has been removed.
Back in 2012 when this answer was originally written, you could usually get away with a synchronous ajax call (async: false) provided it didn't take too long. But you can't reliably do that now (and it was never a good idea, it holds up the UI).

jQuery has unload function:
The unload event is sent to the window element when the user navigates
away from the page. This could mean one of many things. The user could
have clicked on a link to leave the page, or typed in a new URL in the
address bar. The forward and back buttons will trigger the event.
Closing the browser window will cause the event to be triggered. Even
a page reload will first create an unload event.
Note that this should be binded to window object instead of document:
$(window).unload(function() {
// do something
});
You can also bind handler to beforeunload event:
$(window).bind('beforeunload', function() {
// do something, preferably ajax request etc
return 'are you sure?';
});

When a page is reloaded, whatever was there before will be gone. Thus, it seems like what you're talking about is something you'd do at DOMReady or "load" in the new page, since you can't "push" code from the former page into the new context.

HTML page unload is not getting called always in IE

I have an onunload method written on the body of a form. Since the page got large amount contents to be streamed from the server,it takes a while to download the entire form. While the form gets downloaded to the browser,if the user clicks the window close button, the unload event (written to call a server side action to reset some flag) is not getting triggered sometimes. The unload method is written towards the end of the page, is that a reason for this? Is there anyway by which we can make sure that onunload is guaranteed to be called?

The thing that hits you is probably the fact that IE doesn't fire an unload event if window.onload hasn't fired yet. The solution is described in this blog post: http://blog.moxiecode.com/2008/04/08/unload-event-never-fires-in-ie/

There are two reasons. One, like you said, the browser may not even be reaching the unload, so you should declare it above your body tag.
The other is that, as GoldenNewby already stated, you need to give the code some time to finish, such as an alert. This is because the JavaScript is cleared from memory the moment the next page is ready, and execution is simply stopped on the old script. If you can guarantee the script will take less time than a page load, you won't need an alert, but if it could take more than 2ms or so to execute, you will need to buy some time.

IE has an onbeforeunload event, you can use that instead. Just set a flag so that your onunload can exit early if onbeforeunload already did its thing.
window.onunload = window.onbeforeunload = function () {
if (window.isAlreadyUnloaded) return;
window.isAlreadyUnloaded = true;
// do your stuff here.
}