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8 Player Chess

The pawns mostly follow regular chess rules regarding movement. Using the picture above, for the RED player, their right four pawns will advance across the CHROME player and be promoted on the back row of the BROWN player. The same applies for the left four pawns of the BROWN player; advance across CROME and promote when they reach the back row of the RED player. For the left four RED pawns, the same rules apply, they advance across ORANGE and get promoted when they reach the back row of the YELLOW player, and again the same applies for the right four pawns of the YELLOW player, pawns advance across ORANGE and get promoted on the back row of the RED player.
This pattern applies for all players.

If it helps; think of the board as two 'X's where every second player has a direct vertical connection with the players located two to their right and two to their left.. (i.e CHROME will collide with ORANGE & PURPLE. ORANGE will collide with GREEN & CHROME. GREEN will collide with ORANGE & PURPLE. And finally PURPLE will collide with CHROME & GREEN.)

However, while those pawns advance, they are under direct theat from their flanks where the other players move. (e.g The left most CHROME pawn moves up directly in front of RED's pawn line, the second CHROME pawn moves up two spaces in front of RED's pawn line etc. While this may look like a player's pawns leave the player's immediate front exposed to the player directly opposite them, the lateral line movement of chess pieces negate most obvious threats. For rules regarding the centre 'star' of tiles, see the description.)

To answer your other question, for a player's edge most pawns, they cannot capture any pieces until they move from their start location. This doesn't mean they cannot be captured entirely, only when they move from their start location. Again, utilising the above picture, the CHROME player cannot capture the RED player's edge pawn with his own edge pawn unless it moves from its starting location, any other piece CAN capture the edge pawn however. (It would be imbalanced for the CHROME player to capture RED's edge pawn with his own edge pawn and place RED's knight immediately under threat.)

If you have difficulty seeing the pattern, google '4 Player Chess Board' and imagine that layout, but with another four player chess board overlapping it diagonally.

Sorry about the wall of text.

Where do pawns promote? I'm still confused about edge pawns if my edge pawn moves up once then can the enemy edge pawn take it?