Answer to question 1:
There's not as much agreement on piece values in 5D Chess as there is in normal chess. This is partly because 5D Chess piece value is incredibly variable and dependent on the specific position, even more so than in regular chess. However, to give a general idea, one value system that I've seen is as follows: pawn is 1, rook is 3, knight is 5, bishop is also 5 but generally slightly better than the knight, and queen is 15. I can attest that this feels pretty good based on my own competitive experience. And yes, I spoke correctly: the rook is worth less than a knight or a bishop in this game. The bishop and knight can each see at most 4 squares on each board other than the one it's currently on, whereas the rook can see no more than just a single square on each of those boards, due to moving along only one dimension at a time. The rook is good at really long moves, which comes in handy for stuff like Jurassics and time checks, but it has really poor flexibility.
One more note on value: we have to talk about the value of timeline advantage. The maximum number of active timelines that a player can have branched is equal to the number of timelines that the opponent has branched plus one. Active timelines can affect the location of The Present, but inactive timelines cannot. Since the game limits the number of active timelines you can have branched, the ability to branch an active timeline ends up being a highly important resource, and that resource has a value. How much value, exactly? Well, there's once again some argument over this, but consensus is that it's worth more than a queen. Considering that the queen is already insanely powerful in this game, that should really tell you a lot. Just like before, though, we have to consider that this value can vary over the course of the game. Mage, a strong player, has argued that it should be considered a function of how much piece material you currently have: timeline advantage is incredibly valuable when strong pieces like queens and bishops remain on the board, but near-useless in a king and pawn endgame.
Answer to question 2:
Yes, a piece can go forward in time. However, it's not in the way that you seem to think. 5D Chess has two different types of boards: playable boards and history boards. A playable board is a board that hasn't already been moved on. A playable board has a thick outline. If you have a playable board on your turn, then you can move one of your pieces which stands on that board. A playable board is always the rightmost board in a given timeline.
Once a board has been moved on, that board is a history board. A history board has a thin outline. You can't move a piece from a history board, because you've already moved on that board, so you can't "change your mind" about your move. However, you can move a piece onto a history board, which is how you branch a timeline. In a given timeline, every board other than the rightmost board is a history board.
With all this in mind, let's look at the example you gave. You move your queen onto a board square where an enemy king once stood. We'll assume that no one put another piece on that square after the king stood there, since that would block the queen's path through time. In that case, the queen move that you just made is check, at least. It might even be checkmate, though it doesn't have to be. Let's think about exactly why this is check. If you imagine your opponent passing their move, then that creates a playable board on your turn. That board would contain your queen, which you could then move from that playable board back in time to the history board to capture your opponent's king.
Now, we'll look at the second situation. You're playing a game, and it's your turn. There's a playable board that's on your turn, and your queen is standing on a certain square on that board. After you make a move on that board, it becomes a history board, and the game goes on. Later in the game, your opponent moves their king onto the square that your queen previously stood on. No pieces got in the way between then and now. So the question is, can you move your queen from that history board to the playable board where your opponent's king is standing? Well, no, you can't. Since you already moved on that history board, you've lost the ability to move any piece from it. The enemy king is safe.
Due to the way this game works, a piece can't move forward in time within its own timeline. Key words: "within its own timeline". It's entirely possible for one timeline to be more advanced than another one. So, a piece can travel forward in time while also traveling to another timeline.
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???