yes, "chain reactions" are a big part of the game. pushing and climbing rules apply whenever a turtle moves into a space, including when the move was triggered by a push.
yes, for the same reason as above.
no, you may not. the only time you may move one of your turtles off the board directly as your turn action is to score it. you may, however, push your own turtle off the board by moving one of your turtles into it. see example below.
the turtles in that stack that are crossing their far end of the board (i.e. should score) indeed score, and turtles that are being carried back across their starting end of the board are sent back to their nest. see example below.
like the rule of ko in go and the threefold repetition rule in chess, this rule prevents players from repeating the same moves over and over again that may be the best move for both players, such as pushing two turtles back and forth (see example below).
the threefold repetition also applies to this game and end in a draw as well, to prevent a longer loop (more than a back and forth) of optimal moves for both players.
note that a player is only blocked from "undoing" the previous move as their very next move; if they make a move elsewhere, and their opponent responds there, they may now go back and "undo" the original move. in go, this is called a ko fight. in turtles, this is probably very rare.
play the move that you want to play. ☺
probably!
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