I've got two questions about 5d chess with multiverse and timetravel

1. How much is each piece worth?

The bishop has to move in exactly two dimensions. So if he goes backwards in time and in to a parallel dimension thats 2 dimensions, so he cannot move his space. (For the math nerds out there general rule: even number of spatial dimensions; NEVER changes color, odd number of spatial dimensions; CAN change color, but doesn't have to, because odd number of spatial spaces, like the rook its just a straight line in 1D so it can but doesn't have to change color) So when the bishop moves backwards in time and parallel dimension he moves 0 spatial dimensions, 0 is an even number so it just stays the same color because its the same space. The rook moves only 1d but can chose a dimension of the 4 (the game is called 5d chess but there are only 4 dimensions). The queen however can move into ANY amount of dimensions. So when the bishop moves into 2 spatial (like a normal piece) it cannot go backwards in time. The queen however can move like a bishop on the board and still go backwards in time and even into parallel dimension, so it can move much more than bishop and rook combined. So I am wondering how much is the queen worth?

2. Question: I still don't understand wether the pieces can go forwards in time. So if the queen lands on a square where the king previously was, its checkmate. But the king can move onto a square where the queen previously was???