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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.

How to submit a form internally?

I am curious about submitting a form data internally.
Here is an example.
I want to register an account for a website. The website will give a form to register which upon submitting will create an account for me.
But I don't want to go to that site. Instead I'll give a form in my style and collect the same information. Upon submit, I want to create the account automatically. Automatically in the sense, I'll submit the form internally.
The reason why I need this feature is, I don't want my users to create a separate account in another website also. I mean it should save user's time in creating account only. Rest of the things will be taken care by me.
Please let me know if anyone had tried this and had success.
I know it is very difficult for existing accounts and some internal errors. But I also need to track them.
Please let know if this is possible or not.
An Example
There is site called othersite.com which has a form for creating / registering users.
I will a similar form to the user on mysite.com. But upon submit the form information is sent to both mysite.com and othersite.com. Both sites create accounts parallelly with a single form submission.

Unless you are working with AJAX requests and CORS enabled sites, which I assume is not the case, client side technologies ( browser/javascript ) will not help you much to do that.
You have to ask yourself what are the options to integrate with the second site in order to automatically create the account. Following some common patterns used these days:
REST API: You have an url where you can use HTTP to talk to and ask to create the account. Many social networks and other popular services usually expose it. Facebook API
Database: Although it is less recommended you could just insert a new record into the account table if you own and have access to the database used by the second site.
Client Libraries: Some sites provide client libraries so that you can use them together with your project code base. Eg: Twitter Libraries

How to handle this typical case of WebSocket usage?

I wrote a web page where there is a zone for user's comments.
Any authenticated users could post a comment.
As many users could post comments almost simultaneously, I want the comments list to be auto-refreshed.
Thus, I think about using WebSockets.
My thought are about a good/best practice for this use case:
Once a comment is posted, should WebSockets process read the current comments list on database and send a Json response containing all the new comments? This would allow the client to directly append the new comments on the DOM (JS).
Or should WebSocket just check the database (or queue if using a message queue (Redis, RabbitMQ etc..) for instance) and act just like: "Hey, I have new comments, click here if you want to see them !". This solution would only signal the presence of new comments, without bringing all those comments to the client. The workflow of retrieving the events would then involve by the client (by clicking on this sentence for instance) e.g using the traditional Ajax direction: client => server.
It is highly possible that a user posts a comment, then navigates to another page of the website. Therefore, a websocket response containing the whole new comments would be useless. A simple notification would then be possible, as most of known websites do for instance with the "+1" counter or more relevant to the "comments" scenario: "1 new comment available".
Which way should I choose?

I think to decide which data to push is mostly a matter of UI usability / user experience, as opposed to which technology is being used to interact with the server. We should avoid changing the UI with server pushed data in a way that would surprise the user in a negative way, for example having the comment feed constantly growing without any intervention from him.
But in the case of a realtime chart, it's probably better to push the data directly into the chart, that would be what the user expects.
In the case of the comment feed the reason why most sites go with the 'click to load' approach is because of user experience, so I think that is probably the best approach.

I use a combination of both....
In some pages the websocket communication contains the actual data--sort of like a stock ticker update.
And in other cases, the websocket communication just says -- all users viewing xyz data--refresh it. And then the browsers performs an ajax to obtain the new data and the grid is smartly refreshed in such a way that only the changed cells are modified on screen using innerHTML and the new rows are added and deleted rows are removed.
In cases like stackoverflow, it makes sense to show a message, "Got new stuff to show--want to see it?"
When I establish the websocket in the browser, I pass a page Id in the url and the cookies are passed too. So websocket server knows--the user cookie and the page which is being viewed.
Then in the database (or middle tier logic) communicates to the websocket server with messages such as: This message is for users viewing 'xyz' page: smartly refresh grid 'abc'. And the websocket server broadcasts the message.
Because the protocol allows you to pass anything you like, you have the ability to make it anyway you like.
My advise it to do what's best in each particular situation.

Tracking online status?

I am quite new to web development and am working on this social networking site.
Now I want to add functionality to show if a person is online.
Now one of the ways I figure out doing this is by keeping online status bit in the database.
My question is how to do it dynamically. Say the page is loaded and a user (say connection) comes online. How do I dynamically change status of that connection on that page.
I wanted to know if there are any tools(libraries) available for this type of tracking. My site is in python using django framework. I think something can be done using javascript/ jquery . I want to know if I am going in the right direction or is there anything else I should look into?

Create a new model with a last_activity DateTimeField and a OneToOneField to User. Alternatively, if you are subclassing User, using a custom User in django 1.5, or using a user profile, just add the field to that model.
Write a custom middleware that automatically updates the last_activity field for each user on every request.
Write an is_online method in one of your models that uses a timedelta to determine a user's inactivity period to return a boolean for whether they are online. For example, if their last_activity was more than 15 minutes ago, return False.
Write a view that is polled through jQuery ajax to return a particular user's online status.

As Sanjay says, prefer using memory solutions (online statuses have a quite brief use) like the Django cache (Redis or Memcache).
If you want a simple way of updating the online status of an user on an already loaded web page, use any lib like jQuery, AJAX-poll an URL giving the status of an user, and then update the tiny bit of your page showing your wanted status.
Don't poll this page too often, once every 15 seconds seems reasonable.

Implementing web chat, how do I get typing status?

Can someone illustrate how I can get typing status of the other party with JavaScript?
UPDATE
Can someone recommend a one-to-one open source chatting application, preferably written in PHP? I only found open source chatting rooms which are for chatting among all onliners, but I just need a one-to-one chatting.

Here are a list of PHP-based open-source instant messaging software.
Some of those might be relevant for you.

For example, if you had an text area #chat then you could use this code to attach the event:
document.getElementById('chat').addEventListener('keydown', FUNCTION HERE, false);

See http streaming and some ready solutions here: http://ajaxpatterns.org/HTTP_Streaming
this is how google talk does it. And there are ready php or c++ solutions
It was quie a discovery for me!

This is an update to reflect the significant change in the OP's question:
Google Chat and Facebook both use XMPP(jabber) servers, as do most companies I know of that have internal instant messaging.
The nice part about XMPP is that you get all of the "is typing" and other presence-based information without having to roll-your-own in javascript (bear in mind, you will still need to use javascript to pass XMPP requests back to the server, but XMPP has most of the features you'd need already built in).
Check out OpenFire. It's a great XMPP server, totally open source, and they have a web-based version of their Spark client that is pretty nice.
Or you could get a PHP library for XMPP (there are a few). But you'd still need to have the XMPP server running in the background for PHP to work with.
Here's a list of XMPP libraries for PHP from XMPP.org:
Eiffel
JAXL
Lightr
Missus
xmpphp
Or, if you want to keep things mostly browser-side, they also have a list of libraries for javascript:
dojox.xmpp
js.io
JSJaC
strophe.js
xmpp4gwt
xmpp4js

I made a small chat application a while ago, and the only way to do it is to frequently check for new entries in the chat database and fetch anything newer than the last displayed message. At the same time as all that, you can check to see if the user's input is empty. If it is, do nothing. If it isn't, enter a status code into the database beside that user's name. If anyone has that status in the database when you're fetching information about new messages and who is online, you should display the 'user is typing' message. I hope that makes sense...let me know if it isn't.

For User1: If you save the chat message on each key-press to the database, with a status: sent=false and update the last updated date.
For User2: you could pole periodically for the presence of a message where sent=false and use the last updated to update user is typing message. if the lastupdated date is more than a say ten seconds you could remove the message as that person may have stopped typing. This will allow User2 to see User1 typing, stopping and continueing again.
Ideally polling for this information will be part of an existing call to the database to reduce additional overhead.