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packaging django application and deploying it locally

I've never worked with Django before so forgive me if a question sounds stupid.
I need to develop a web application, but I do not want to deploy it on a server. I need to package it, so that others would "install" it on their machine and run it. Why I want to do it this way? There are many reasons, which I don't want to go into right now. My question is: can I do it? If yes, then how?

This is possible. However, the client machine would need to be equipped with the correct technologies for this to work.
When you launch a web app on a server (live), the server is required to have certain settings and installs. For example, a Django web app: the server must have a version of Django installed.
Hence, whichever machine is running your web app, must have Django installed. It presumably also needs to have the database too. It might be quite a hassling process but it's possible.
Just like as a developer, you may have multiple users working on 1 project. So, they all need to have that project 'installed' on their devices so they can run it locally.

You need to either use a python to executable program, with Django already in it. The website files you can place into the dist folder or whatever folder has the executable in it. Then you can compress it and share it with others (who have the same OS as you).
For an example:
You have this script in Django (I'm too lazy to actually write one), and you want to share it with someone who doesn't have Python and Django on his/her computer.

How to use python to do the web development (or how to set uo cgi)

As the title said, just wonderring how to use python or anyhow to include executable python script into HTML

Using django to do this.
django official web:
https://www.djangoproject.com/

I would look into the python documentation here for learning about Python in the web. But more specifically, there is documentation here explaining Common Gateway Interface (CGI) and how to use it. I recommend looking into this first because I am unsure what exactly you need help with, if it is simply wondering how it works, then these links will explain that just fine.

Flask is very simple micro framework for writing web applications in python.
http://flask.pocoo.org

adding browser capability to an existing python script

In essence I want to run existing python scripts through a web browser, display the text and plots(if any) and also keeping the ability to run them through the command line.
I am wondering is there any toolkit that can help me with the development.Also it would be nice if the toolkit does or allows JavaScript based interactive plots.
Thanks!
-Abhi

WSGI is designed for just this purpose - it provides an interface for a web server to initiate python scripts.
You probably don't want to work with WSGI in the raw. Flask is a straightforward, simple framework you might use for this.
The details of how to actually build a WSGI web server are well beyond the scope of a stackoverflow answer - you can find plenty of tutorial docs on Flask's website.

RESTful Web service or API for a Python program in WebFaction

I have developed a few python programs that I want to make available online.
I am new to web services, and I am not sure what I need to do in order to create a service where somebody makes a request to an URL (for example), and the URL triggers a Python program that displays something in the user's browser, or a set of inputs are given to the program via browser, and then python does whatver it is supposed to do.
I was playing with the google app engine, which runs fine with the tutorial, and was planning to use it becuase it looks easy, but the problem with GAE is that it does not work well (or does not work at all) with some libraries that I plan to use.
I guess what I am trying to do is some sort of API using my WebFaction account.
Can anybody point me in the right directions? What choices do I have in WebFaction? What are the easiest tools available?
Thank you very much for your help in advance.
Cheers

Well, your question is a little bit generic, but here are a few pointers/tips:
Webfaction allows you to install pretty much anything you want (you need to compile it / or ask the admins to install some CentOS package for you).
They provide some default Apache server with mod_wsgi, so you can run web2py, Django or any other wsgi frameworks.
Most popular Python web frameworks have available installers in Webfaction (web2py, django...), so I would recommend you to go with one of them.
I would also install supervisord to keep your service running after some reboot/crash/problem.
I would be glad to help you if you have any specific question...

Whats the recipe for a safe enviroment to create/play with my web applications.

How can i create a safe environment to create new and play with my web applications?
My ingredients so far: python,flask,github,heroku --- I have effectively created a app using flask and heroku (it just says hello world)
I have some knowledge of python. Have read through but hardly understand the flaskr tutorial for Flask. I do however envision that i'm going to be very frustrated if i can't have some kind of version history of my stumblings.
Without being sure i feel like the recipe might include: Github and virtualenv and some coping pasting of directories...
whats a recommended way to do this?

Just setup a GitHub repository and start hacking away with Flask.
Some pointers:
Use SQLAlchemy for database operations. It's secure and easy to use.
Either dive right into your project or make some simple test ones with Flask. It's a really beautiful framework to work with and is easy to learn, so just try to accomplish some simple tasks and get used to how it works.

I suggest you to use virtualenv and virtualenvwrapper, this way you can work on isolated pythons without filling your system's python with many eggs and switch between them easily.