No, a king can move one square in any direction on its first move or it can 'castle.'
The pawn is the only piece that is restricted to forward-only movement. The pawn may only move forward (toward the enemy), one square at a time, unless it's making an opening move, in which case it can move one or two squares.
The pawn can only change direction to take a piece -- a pawn can take a piece that is one square forward diagonally (that is, up and right, or up and left one square). The pawn cannot take a piece directly in front of it.
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