List of Pieces used for Bulldog and Infinite Chess

Two thoughts 

1. So it can move like a queen+knight normally?

2. That seems OP

Moves in any direction ... 

  This is a list of pieces used for Bulldog chess and Infinite chess:

• Guard (G) - Moves and captures like a king.
• Witch(W) - The witch is transparent to friendly pieces, and she also makes all adjacent pieces (friend and foe) transparent to friendly pieces (but pieces are not transparent for the witch). The witch does not capture other pieces, but she can be captured. Although pieces are not transparent to the witch, she is very agile; she combines the movement of queen, knight, and can jump orthogonally and diagonally two squares. Transparency of a piece means that other pieces can move, attack, and capture right through the piece.
• Spirit (S) - A spirit moves as a knight. It can 'capture' friendly pieces, which gain the movement of a knight in addition to it's other abilities (knights are not affected, but can be used for transportation. A 'possessed' piece can be captured like normal. A spirit which is not possessing anything can only be captured by a possessed piece. It is transparent to friendly pieces.
• Hunter (H) - Moves as king when it does not capture. However it captures twelve squares as shown in diagram below:

   

Also here's a different and maybe more clear description by evert823:The Hunter moves as a King when he does not capture.
But when he does capture, he moves like a Knight or orthogonally exactly two squares. While doing so, the Hunter is allowed to jump.

• Time Thief  

  (TT) - The Time Thief moves like a Queen, but does not have a normal capture. The Time Thief has a special move that is done in 2 steps.

  1. Undo your opponents previous move (restore position to exactly the same as before, which might include putting back a captured piece).
  2. Move your time thief (like a queen) and capture the piece that moved on your opponents previous turn.

  The Time Thief may not undo a move if the Time Thief was captured or if it is unable to capture the piece that moved after undoing the move.

  Note that this means the Time Thief must "see" the piece before it moved.

  From this it follows, that a King in reach of a Time Thief would put himself into check by moving away.

  [ADDED BY @evert823] The rules for Time Thief include rules for conditional check, which haven't been mentioned above. Conditional check means that a King can be captured, but thereafter be restored by the Time Thief in such a way that the King will no longer be in check or again in conditional check.
• Joker

  (J) - Moves and captures like the last piece with which the opponent has moved. But does not inherit any special functions. A Joker who is imitating a Crippled Amazon, can move like a Queen, if he is a Knight's move away from another friendly Crippled Amazon. That other Crippled Amazon does not get the Queen's move from the presence of the Joker, and a Joker cannot move like Crippled Amazon if he is a knight's move away only from another Joker, not a Crippled Amazon. A Joker who is imitating a Time Thief moves and like a normal Queen but does not capture.

  A Joker who imitates a pawn can move 2 squares if he is on his 2nd rank.

  Crippled Amazons (CA) - Moves and captures like a Knight. When two Crippled Amazons of the same color are separated by a Knight's move, they can temporarily move, capture and give check like an Amazon (Q-N compound) until one of them moves out of such a position or is captured.
• Werewolf  (W) - The Werewolf moves as a Queen, but over a maximum distance of 3 squares only (i.e. from d1 you could play Wd4, if the intervening squares are empty, but never Wd5). But it can also directly leap to the second square, if it wants to end there (i.e. you can play Wd1-d3 even when d2 is still present). If it makes such a leap, it can optionally capture the enemy piece it leaps over, (in the Checkers way, as it were), possibly in addition to what it captures on the destination square in the normal way.

  A Werewolf is thus capable of double capture! This makes it stronger than an ordinary Queen. (The non-capturing leap to the second square already compensates for the missing distant moves.) It can also capture protected pieces with impunity, by jumping over them to a safe square on their other side.

  Now this game would not be very interesting if the Werewolves could be quickly traded, leaving you with a boring normal Chess end-game. Fortunately this cannot happen, because Werewolves are almost immortal! Only Kings can kill them, as only these can afford the silver weaponry needed to do the job. But when a non-royal piece captures a Werewolf, it becomes one. (Technically: the attack is suicide, but 'turns' the Werewolf, which fights on your side after it.) As Kings normally don't participate in middle-game tactics, this guarantees survival of at least one Werewolf until the end-game. (One can disappear from the game when Werewolves capture each other.)

• Dwarf (D) 

  Moves and captures like a king (but not royal). The Dwarf can only be captured when it is attacked by two or more pieces. One of the attacking pieces is allowed to be pinned on the king. The case of doubled Rooks (Bishops/Queens) must be explicitly mentioned here: assuming that the rear Rook cannot jump over the front Rook, the rear Rook does not count as attacking the Dwarf.

• Xianqi Cannon (C) 

  The Cannon (from Chinese Chess or Xiangqi) moves like a Rook. But in order to capture it must jump over another piece. If it does not intend to capture then it cannot jump.

  (So far this is the general rule as known from Xiangqi. But now that the Cannon appears together with the Witch, one more remark must be made here: In order to capture, the Cannon must jump over another piece which is non-transparent for that Cannon. Without capturing, the Cannon can of course jump over a transparent piece to an onuccupied square.)

• Bulldog (D) - Moves and attacks the same as a pawn, except pieces FROM ITS OWN ARMY ONLY can pass over it in any direction. If a bull dog reaches the 8th rank it can immediately move to any square in the first four ranks (but cannot capture a piece during this move). This move can only be completed during the same move it reaches the 8th rank. (If this option is not taken, the right to do so later is forfeited). The bulldog does not promote to other pieces as pawns do.
• Zombie (Z) - Slides up to two squares in a rook's direction (cannot jump). The zombie can not capture pieces, but "scares" enemy pieces with fright instead. All enemy pieces within its attack range are frozen and cannot move. Pieces remain frozen until the zombie moves, is captured or blocked. A king may move into the line of attack from a piece immobilized by a zombie. Likewise, a king may move out of the range of an immobilized Time Thief safely.
• Hawk (H) - Leaps exactly 2 or 3 squares in any orthogonal or diagonal direction. The leaping move means it can jump over other pieces.
• Chancellor (C) - Moves and captures as rook + knight.
• Cat/Mouse Mouse (M) - Moves like a rook, "scares" enemy pieces (except cat and mouse) on adjacent squares, rendering them powerless (cannot capture). Pieces next to the enemy mouse can move, but only to a vacant square. Pieces next to the enemy mouse (except cat) cannot deliver check. The mouse can only capture the enemy mouse, and only then if it's on an adjacent square (captures like a king). The mouse is not "scared" of the enemy mouse, therefore it is unaffected by being next to it.

  Note the king and pawns cannot capture an enemy mouse. Other pieces can. 

  Cat (C)

  Moves to a vacant square by jumping two squares in any direction, and captures like a king. The cat can capture any piece, and is not scared of the mouse. The cat cannot capture by jumping, and it cannot move to an adjacent vacant square.

  Castling... same as normal, except king moves three in either direction. Also, the king cannot pass through check, but if an enemy piece that would otherwise stop castling is next to mouse, then the king can "pass" through this check, and even land on the square that is "controlled", since the control only exists when the mouse no longer cripples the piece.

• Angel (A) - The angel makes all friendly adjacent pieces immune from capture. The angel does not capture other pieces, but she can be captured. The angel combines the movement of queen, knight, and can jump orthogonally and diagonally two squares. A king which is adjacent to his angel is not subject to check or being checkmated, and a king can move next to his angel even if the square is under attack. [ADDED BY EVERT823] The Angel makes friendly adjacent pieces immune, not only from capture, but also from all other side  influences by other weird pieces. So she would also protect from the freezing abilities, and from the spells of the Witch.
• Ball 

  (Ball): Moves and captures as a rook. In addition the ball can leap up to three squares away (capturing a piece on the square it lands on). When leaping, the ball stops on the square it lands on (does not continue moving as a rook).

  Also, the ball wraps across the board. For example, the ball can roll off the board at left and appear on the same rank at the right. (allowed for both jumps and sliding).
  In the diagram arrows are leaps, circles are sliding. Note that the ball can slide left and land on j4.

  After the ball has moved at least once, the ball paralyzes pieces by a rolling attack: All opponent pieces attacked by the rook's move (sliding attack) are paralyzed. This means that a piece attacked by the ball as a rook are frozen in position while the ball remains in position. This includes the ball's wrapping ability (and therefore both player's guards are frozen in the games opening position).

• Cougar (C) The Cougar can always move as a bishop. When it is on a black square, it can also move as a knight, and when it is on a white square, it can also move as a rook.
• Jaguar (J) The Jaguar can always move as a rook. When it is on a black square, it can also move as a bishop, and when it is on a white square, it can also move as a knight.
• Harpy (H) - A Harpy moves as a Queen + Knight.  It may be captured, but it cannot capture enemy pieces.  It captures one of its own pieces and drops it on the board within two moves (if legal, e.g., if the king is in an unblockable check, you may wait until next move.  If the check can be blocked, you must block the check by dropping the piece if it is the second move since the Harpy began to 'carry' the piece.)  Pieces may be dropped on any unoccupied square, as in Bughouse and Crazyhouse.  Pawns may not be dropped on the first or eighth ranks.
• Musketeer pieces in general
• Lumberjack

   

   

   

   (L) - This piece moves like a Queen and cannot jump over other pieces. The Lumberjack also cannot capture an enemy piece by landing on the square that the enemy piece is currently occupying, though the lumberjack can be captured normally. The special ability of the lumberjack is that wherever it lands, all enemy pieces that are horizontally or vertically (not diagonally) adjacent to the lumberjack get knocked away one square in that direction. If the knockback square is occupied or is past the end of the board, the piece is captured.
• Siege Tower Same as bulldog
• Tree  (Tr)

   

  The Tree can move one step orthogonally, cannot capture, and can be captured. Having your Tree captured is of no further consequence.
  It's mandatory, always at the end of your turn, to have your Tree orthogonally adjacent to at least one friendly piece. So any move that does not result into this circumstance counts as 
  illegal.
  A player who has no Tree does not have this obligation. A piece can give check despite being hampered by this obligation!

  (For further convenience, we will call a Tree without any orthogonally adjacent friendly piece an abandoned Tree. Moving your piece orthogonally adjacent to your abandoned Tree - or vice 
  versa - will be referred to as reconnecting to your Tree.)

  All other rules of Chess apply, including rules regarding check, mate and stalemate.
  Exception: If a player is not in check, and has an abandoned Tree, and has no legal move to reconnect to his/her Tree, then it is not stalemate, but that player loses.

PLEASE NOTE: I COULDN'T FIND THE ORIGINAL PICS OF SOME OF THE PIECES. SO SORRY.

      I am sure I missed some so tell which. I will try to update with the rules as well.