For Twitter you just use basic authentication, by setting the authentication header. Not sure about Facebook.

Is there anyway we can display web page, i.e. for facebook connect, some sort of webkit available in adobe air.

No, there is no way. This has been discussed quite a bit in previous posts, so I won't go into detail. However, there are obstacles to displaying web content/HTML on a TV that does not provide a pointing device(mouse, finger, etc). How would you click a link for instance without a pointing device? You could maybe use spatial navigation, but having to navigate through all the links in a page just to get to the one I want is not an ideal situation.

Also, I doubt any OEM would approve multiple Twitter or Facebook widgets for their platform, at this point, since they already have the main brands on board...