Is it possible to have a client app which can authenticate using Facebook but without requiring browser(I mean no embedded browser in the code)?? User inputs the username/passwo
Actually the answer is absolutely not.
In order to authorize your app a user has to enter their facebook username and facebook password on facebook site and you need web browser for this. There is no way to skip this step (you can't ask what their username and password are and then exchange it automatically for access token). You can read more about this here.