Diagonal movement is allowed through the corners of spaces that do not share any sides, and diagonal movement in the same direction goes through the corners at opposite ends of spaces.
Let me understand this correctly: A bishop on e8 moves in the direction of switch A4/a4. Further down in your description you say that in this case the bishop can only reach A4. But the bishop reaches the same corner of A4 and a4; therefore the bishop can decide whether to stop on A4 or a4.
So, in principle, a move into the switch, no matter from which direction and valid for all pieces, must result in a decision between the two squares of the switch - provided that the switch is not occupied.
My description for this is:
Finally, you can move into a switch from below, from the side or from above. If the switch is not occupied, then you can choose whether the piece that moves into the switch is on 4 or a4 or 5 or h5 after the move. If the switch is occupied, then the piece in the switch must be captured; the opponent’s piece takes the place of the captured piece.
2. While some paths can lead to either Switch, others lead to only one space or the other in a Switch. For example, a Bishop on e8 can go to A4 or h5, and a Bishop on d1 can go to a4 or H5.
See the comments above.
A bishop on e8 or d1 can move to A4 or a4 respectively to h5 or H5.
Also, a Bishop on A4 can move away on either light or dark spaces, but one on a4 can move away only on light spaces.
But a bishop on A4 cannot move to f8. For that he would have to be on a4.
3. ... or one is occupied by an enemy piece. If a piece moves to the empty space in a Switch, and the other space is occupied by an enemy piece, that piece is considered captured.
A piece can only be captured on the square it stands. Therefore, in an occupied switch, you cannot move to the empty square and capture the piece on the other square of the switch. After the move into the occupied switch, the capturing piece stands on the square of the captured piece.
The Knight can leap directly to any space that could be reached in two one-space moves except for those reachable by two in the same direction.
I am not sure if the rule is correct. In my description I use a definition which comes from Alfred Pfeiffer (Chemnitzer Schachverband e.V.):
The knight moves to one of the squares that a king can reach from the square in two moves, but which are not on the same row, line or diagonal. It does not move across squares that lie in between.
Let me understand this correctly: A bishop on e8 moves in the direction of switch A4/a4. Further down in your description you say that in this case the bishop can only reach A4. But the bishop reaches the same corner of A4 and a4; therefore the bishop can decide whether to stop on A4 or a4.
So, in principle, a move into the switch, no matter from which direction and valid for all pieces, must result in a decision between the two squares of the switch - provided that the switch is not occupied.
My description for this is:
See the comments above.
A bishop on e8 or d1 can move to A4 or a4 respectively to h5 or H5.
But a bishop on A4 cannot move to f8. For that he would have to be on a4.
A piece can only be captured on the square it stands. Therefore, in an occupied switch, you cannot move to the empty square and capture the piece on the other square of the switch. After the move into the occupied switch, the capturing piece stands on the square of the captured piece.
I am not sure if the rule is correct. In my description I use a definition which comes from Alfred Pfeiffer (Chemnitzer Schachverband e.V.):