I use the official Facebook SDK in my Android Application. After the user logs in, I can get the uid and the name of the facebook user like so:
Facebook mFac
ImageView user_picture;
userpicture=(ImageView)findViewById(R.id.userpicture);
URL img_value = null;
img_value = new URL("http://graph.facebook.com/"+id+"/picture?type=large");
Bitmap mIcon1 = BitmapFactory.decodeStream(img_value.openConnection().getInputStream());
userpicture.setImageBitmap(mIcon1);
where ID is ur profile ID...