Quoridor rules when faced the opponent
According the rules, You may only place next to the opponent's pawn (i.e. you may only "move diagonally") if there is a fence behind the said pawn. Note how the diagonal squares are not permissible destinations in figures 2, 3 and 6. Only when the oppenent's pawn is backed by a board (figures 8 and 9) is the diagonal move permissible.

As such, diagonal movement is not allowed in the scenarios in the question, so your first image is incorrect, and your second and third images are correct.