Load form data in JavaScript and run something client side
It's very unclear what you are looking for. If the question is about server push keywords are WebSockets,Socket.io,Ajax,Comet,Bayeux to start with
The original framework of my app (using Python) is below:

user key in keywords in forms.
App use the data in forms as parameter to get some results from third-party website.
The result which is from third-party website will be analyzed in my app.
Then show the result of analyze to user.

But there are some problems between my app and third-party website, so I want to change the framework of my app.

user key in keywords in forms.
store the keywords which in forms as cookie.
automatically download one javascript which in my app (website), and run the javascript in user's computer.
the javascript will get result from third-party website, and then sent the result to my app.
my app will analyze the result (from third-party website) and then show the result of analyze to user.

I want to know how can I do this, or what keyword should I search in Google.