Why the black king can't eat a white rook because white kinght can't move and protect the rook?
A king can never move into a square attacked by an opponent's piece; that is it can never move into check.
Pinned pieces still cover squares they normally can move to, regardless of if they are pinned or not. Think about it this way. If you were allowed to expose your king to an attack, your opponent could as well and just take your king, ending the game.
Why the black king can't eat a white rook because white kinght can't move and protect the rook?