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.
Correct.
But the bishop reaches the same corner of A4 and a4; therefore the bishop can decide whether to stop on A4 or a4.
No, it cannot. Let me break the move down into steps. First, the Bishop on e8 moves to d7. At this point, movement in the same direction must go through the opposite corner is just passed through. This is the corner that d7 shares with c6. Continuing in the same direction, it can go to b5. At b5, it can move diagonally to A4, because b5 and A4 share a corner but no sides. Also, this is in the same direction that the move from e8 to b5 was in. However, b5 and a4 do share a side, which means that movement from one to the other is not diagonal. So, a move from e8 to a4 would be illegal.
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.
No, that is completely the opposite of how I understand the rules.
A bishop on e8 or d1 can move to A4 or a4 respectively to h5 or H5.
This is unintelligible. If you mean what you said above, it is contrary to my understanding of the rules.
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.
That is correct, and I didn't say anything to the contrary. The light path from A4 goes through b3, c2, and d1.
... 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.
Are you saying that a piece cannot capture a piece in a Switch unless it can move to the space the piece is on? Or are you saying that when a piece can move to either space in a Switch, it can move to the Switch and capture the piece, and then it must occupy the space the piece was on?
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.
They are the same, but I removed the ambiguities in his description and used some technical language. Since the King cannot move into check, and a Knight is not subject to the same restriction, I replaced the reference to two King moves with one to two one-space moves. Since I would normally refer to ranks and files rather than to rows and lines, and since I have been using these words in an algebraic sense rather than a geometric sense, I rewrote it to not use them. To "leap directly" is technical terminology that implies that a move "does not move across squares that lie in between."
Correct.
No, it cannot. Let me break the move down into steps. First, the Bishop on e8 moves to d7. At this point, movement in the same direction must go through the opposite corner is just passed through. This is the corner that d7 shares with c6. Continuing in the same direction, it can go to b5. At b5, it can move diagonally to A4, because b5 and A4 share a corner but no sides. Also, this is in the same direction that the move from e8 to b5 was in. However, b5 and a4 do share a side, which means that movement from one to the other is not diagonal. So, a move from e8 to a4 would be illegal.
No, that is completely the opposite of how I understand the rules.
This is unintelligible. If you mean what you said above, it is contrary to my understanding of the rules.
That is correct, and I didn't say anything to the contrary. The light path from A4 goes through b3, c2, and d1.
Are you saying that a piece cannot capture a piece in a Switch unless it can move to the space the piece is on? Or are you saying that when a piece can move to either space in a Switch, it can move to the Switch and capture the piece, and then it must occupy the space the piece was on?
They are the same, but I removed the ambiguities in his description and used some technical language. Since the King cannot move into check, and a Knight is not subject to the same restriction, I replaced the reference to two King moves with one to two one-space moves. Since I would normally refer to ranks and files rather than to rows and lines, and since I have been using these words in an algebraic sense rather than a geometric sense, I rewrote it to not use them. To "leap directly" is technical terminology that implies that a move "does not move across squares that lie in between."