Is it possible to create a completly develop a UI in other technology like ExtJS

You should be able to. The API's allows you to do a lot. But the big question is.. Why? Appian is a framework and its purpose is easy building, flexible modeling and device independent execution. You lose all the flexibilities that you get out of the framework. Which leads to an interesting question - what are you trying to achieve by doing this?

Why i am thinking in this direction because among our client base there are sole clients want to use their existing UI applications to integrate with appian.This means that a process will be initiated by an external UI and data will be fetched or stored from/to appian process from this external UI web application.

Starting a process from an external system and interacting with data during the workflow is a common use case. There are other ways of achieving the same instead of building the entire solution based on API's. I suggest you speak to Appian professional services who could guide you in the right direction.