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AJAX - How can I build a notification system, that is constantly getting updated, without slowing down my website too much?

I am a beginner to web development, and I am trying to do a notification system with AJAX and jQuery.
In my web application, I have a comment system where you can mention another user. After a comment mentioning a certain user has been written, a new entry on my notifications table will be added, containing the comment, the id of the user who commented and the id of the user(s) who will receive the comment. After the notification is stored in the database, I want the person that was mentioned to receive the notification.
To that effect, I decided to use AJAX. Using the setTimeout() method, I am sending an AJAX request to the database every 2 seconds, and with that, I can display the notifications visually to the user that is meant to receive them.
My only concern is that this will slow down the site once I connect it with a server.
So, I was looking for a way that would allow me to implement a notifications system without slowing the site too much, since the one that I am using currently doesn't seem very efficient.
I would appreciate any help.

Is that even feasable?: user click on a button on my website -> get data from another website -> display this data on my website

I tried to be the most explicit possible and I know I can do it in python but i'm trying to do it in javascript.
the data is in sms/tweet style and length so not very huge and I know where it's located on the other website

If the website you want to scrape is configured to allow cross-origin resource sharing (CORS), you can have the client scrape it.
Otherwise, your own server will have to perform the scraping then send it to the client.

How do I push mongodb data?

So I have developed a web app as a hobby on Handlebars, Express and Mongoose/MongoDB.
The app let's users create an account and then post advertisements for other users to see and respond to.
All the ads posted by users show up on the index page. So it is common view for all the users on this web app. I am relatively new to web development so to build such a simple app it took me a while but boy I learned a lot!
Now the issue I am facing is, when a user A posts an Ad while the user B is logged in and is currently on the index page (a page that lists all the ads posted) it won't show up for user B unless user B refreshes the page. Rightly so actually because only when the index page's route is hit it will query all the ads and refreshing is basically hitting the index route I get that. But I don't want it that way. I want it to show the new ad on user B's index and pretty much every user's index if there's new ad by any user.
So I did a little research/reading and I learned that I can do it by learning to work with triggers on mongodb and like create some kind of trigger that when a new ad is posted do something. I like the idea but failed to find resources to learn how to use such a thing.
The other option I was suggested was to use socket.io but that too I can't grasp how can I make an entire Ad document work as a socket. I am lost and implementing this feature of dynamically loading ads for all users will complete this hobby project of mine and will help me find a junior dev job in local community.
I request stackoverflow's community to guide me how do I go about doing this and what resources I can use to learn about it.

The socket.io seems to be the best solution for your case. What you will want to do with socket.io is every time a user posts an Ad you use socket.io to notify the rest of the users that there is an update.
If you don't want to send the entire document using the socket you can use the socket to notify the clients and on the client side every time you receive such a notice from the server you will either
a) Refresh the page(not suggested as it will make the user experience unpleasant) which is easier to implement
OR
b) You can use an Ajax request to get the new data from your server and update the fields on the fly(which makes for a better user experience).

Best Way You can come with using Short Polling concept from client side to ask for new data after 1 or 2 seconds (whatsoever count to need ) . Gmail for new inbox mails also uses sync method in a particular fashion . Just ask from server for new data
OR Second option to go through below
On Server Side
Serve index.html page to User A (which is logged in now).Some User B inserts data
Maintain a function or a cron job (checks the count of Total Ads ) Lets say after every 1 minute or so
If there is change in count from the previous total_count , update it and get new mlab documents and send it to function , Let's say push_new_ads which will be sync via socket.io to client
On Client Side
Sync your client_total_count with server_local_count push_new_ads using socket.io and If there is change in count , make a simple fetch api call to get data and appends it to previously fetched array
There is no such way to directly listen the changes in mongodb But you can trigger some changes from oplog using tailable cursors

Posting data dynamically without refreshing the page

I just want to know how can I post data without refreshing the page for example, now Facebook when you post a comment it will be posted and shown to the people without refreshing the page. I do know how to insert data in MySQL without refreshing the page with AJAX but the question is: how to insert the data and get it at the same time without refreshing the page.
Thank You

OSDM's answer might seem accomplish the behavior you want but it isn't the one you're asking about. His answer would only provide updates when a user upload's something and not as they are created in the system (uploaded).
There are 2 different ways you can accomplish the fetching of new information in the server: AJAX and WebSockets.
AJAX - AJAX stands for Asynchronous Javascript and XML. It allows you to fetch content with a particular server behind the scene and then you can insert the newly fetched data into your page to display it to the user. This however has to be manually triggered and therefore doesn't really happen in real time. You could trigger the fetching of data either manually (e.g. with the press of a button), or on a timer (e.g. every 5 seconds, 10 minutes, etc). It is important to note that it is hard for the server to know what information the page is currently displaying and therefore each AJAX call usually request all of the information to be displayed and re-render the page (deletes the current content and inserts the newly fetched one which also includes content that was already being displayed).
WebSockets - WebSockets can be thought of as an 'upgraded' HTTP connection. The client and the server establish a connection and are free to send data in either direction. You can set up web sockets between your server and the website (client) such that whenever new content is inserted into the MySQL database the server relays the new content to the client. Much like AJAX, you would interpret the new information and add it to the page. The upside of using web sockets is that information is being fed to you in-real time as the server receives it. This means that you only need to fetch data in bulk when you first load the site and updates are pushed to you as they occur. You do not need to rely on a timer or manual input to fetch data as you're being fed data and not fetching it.
Facebook, for example, doesn't rely on a timer or you fetching new data (although that certainly happens if you refresh the page) but each client is listening to the server for new information through web sockets.

That is all javascript (or jquery). You allready know how to send the data to your server. Now all you need to do is modify the html with javascript.
For example(jquery):
$("#submit").click(function(){
$("#comments").append("<div class=newcomment>"+$("#textbox").val()+"</div>");
$.POST('upload.php',{comments:$("#textbox").val()});
});
Now the comment is send to the upload.php and the comment is added to the comment section of your page.
If you need data from the server also to be included, just add some javascript to upload.php file and do something like this: $("#getdatefromserver").load('upload.php',{comments:$("#textbox").val()}); Now the javascript from upload.php will run in the page.
And no page refresh is done.

Check if user Likes Page with JS API?

I know this has been asked a bunch of times, but I have only seen serverside solutions.
I'm running an iframe app that is embedded into a page as a tab. I want be test to see if the page is liked or not without prompting the user for anything.
Is there a way to do this with just JavaScript? The platoform we are building on is ASPX and I dont really have the option of going serverside.

Its not available because you need to inspect the http post parameter called signed_request and this isn't available on the client side. If the user has authenticated with your app and given you permissions to read their likes/interests, then you could then check with javascript api but I'm guessing you wouldn't want to make them approve your app just for this.