Is it allowed to build a bridge with a piece which has its Pünct in its middle? I mean: may I move piece with its Pünct in its center to a place where the Pünct is over my own color, but on a lower level?
You may do so. A general rule is: it is always what you can see from above that counts. This goes for completing a connection as well as for moving pieces on top of other pieces. So, it is allowed to make a bridge with the PÜNCT in the center of a straight or an angular piece, as long as it bridges a space that is already yours (no matter whether it is occupied by the PÜNCT of another piece or by a secondary dot).
Who wins when a player completes a connection for himself and for his opponent with one and the same move? For example: Black has a piece stacked and blocking White's connection. On his turn, he moves the stacked piece to make a connection for himself. And by moving the piece, he unblocks White's connection. Since both players now have a connection, is the game a draw? Or since it was Black's turn, does she win?
As for GIPF and for YINSH, it is the player who causes the situation who wins. In the case mentioned in the example, Black is the winner.
What if players start repeting moves?
For the time being: the games ends in a draw.