Can anyone tell me use of Ajax? Is it for UI development also or just for small part of data processing?
What I see on various sources is that there are various libraries available also like ext, DOJO, YUI (Yahoo User Interface), GWT (Google Web Toolkit).
Can anyone tell differences briefly among there and their purpose?
GWT isn't mainly for running on GAE; it's for people that want to wrap up their client-side code in Java. Whether or not that's a good idea is a different issue.
Each have their advantages and disadvantages, and which is chosen may depend on individual preferences as well as technical requirements.