Can I use MonkeyRunner tool to work in mobile as application
I want to simulate touch event, keyboard event on mobile device. Can I do it with MonkeyRunner? 

From your development machine, yes. Per your question title, you cannot use MonkeyRunner on a device.

Also, I have the impression that it only works with SDK?

Yes.

I want the application to be installed on mobile, which will perform some random touch, keyboard events. Is it possible with MonkeyRunner?

Fortunately, no, as this would be a massive security hole.
I want to simulate touch event, keyboard event on mobile device. Can I do it with MonkeyRunner? Also, I have the impression that it only works with SDK?
I want the application to be installed on mobile, which will perform some random touch, keyboard events. Is it possible with MonkeyRunner?
If yes, please provide me help on how to start writing python for mobile, and how to make project for android in Python. I have used Eclipse for java for android, but not for python.