Let's invent some very weird pieces

Amazon. You are literally describing an Amazon

fogr master can move like any chesspiece every Fairey piece it is worth 30 points so it is the most powerful piece

Soviet Man- Can move every direction only up to 4 squares. If it captures a piece it nukes the board and all the pieces surrounding the captured piece blow up. No chain explosions.

Bear
Can make two king moves in a row. He can capture only from the second king move. Can make a self-removal-get out of the board to sleep in the den, where it sleeps for 5 moves, and after they expire must be put back on the board.

How about a Hoplite?

It can move two squares sideward and the only way for it to move forward is by eating a piece in front of it.

Vampire- has the moves of a pawn in shogi (Moves forward 1 square/turn) but also captures forward and anything it captures turns into a piece on its side.

Cow: Moves and captures like a king, but any of your own pieces that happen to be next to it can drink milk and make two moves in a row, as milk gives power.

Lizard. Moves and captures like a knight 3,1 + knight 3,2, or Camel+Zebra.

A TERRORIST. Moves in a straight line on 1 or 2 squares. It does not capture the opponent's pieces, but blows them up. If, after the terrorist's turn, there are pieces of a different color within the same square, they all explode, while the terrorist himself does not explode. The explosion of the opponent's king - the loss of the game.

TRAITOR-moves and captures like a king, gives up if he is attacked by the opposite piece, switching to the other player's side.

Time rewinder: moves like a king, no special capture move, instead of capturing enemy pieces, morphs them into lost-in-time pieces, can't check, morph kings or be turned into lost-in-time time rewinder, can be captured by time rewinder.

Lost-in-time piece: can't be controled by player, can't be captured, can capture both teams' pieces, repeats its moves in a reversed order (every lost-in-time piece moves once at the beginning of its color turn) until it has no more moves to repeat, then it morphs back to its normal state.

Edit: Every lost-in-time piece's move restores turn and game time that got spent and steals all the time that was given for making the move that piece actually reverses. Time rewinder would probably have value of 10 but I'm not sure.

A Spiral Mover: this is a slider that moves along trajectories that wrap around it like a spiral. It can potentially attack every square on the board, but only when the board is empty, and it is not close to an edge. But it is very easily blocked:

I proposed a chess variant that uses this type of move for the King (but otherwise does not differ from orthodox Chess). Because Kings cannot be traded out of the game this ensures it will never degenerate into normal Chess. The idea is that this should reduce the draw rate very much, as even in a bare King vs bare King end-game there are (forcible) checkmates. (E.g. black is checkmated in the shown position.)

This is actually very interesting. My first thought was it's hard to visualize the path, but maybe it's less hard than I think. That makes it a very well playable piece. I'm not really enthousiastic about turning the King into a Spiral Mover. But a Spiral Mover as additional piece is really interesting.

You could add the diagonal version of the Spiral Mover.

It is not too difficult; there is a short-cut compared to tracing out the entire spiral. You just take the largest empty square area centered on the piece (every square in there can be reached). The ring of squares around that will be entered by the various spirals (there are 8, depending on starting and wrapping direction) on the squares next to the corners, and move 'inward' from there:

Backtracker: can move and capture like a wazir and move without capturing on squares visited by him previously if they are free

My new idea is Dragon Egg

For the first 10 moves, it moves and captures like a king. But after 10 moves, the egg must hatch into a dragon that moves as a knight and pawn. A dragon, unlike a pawn, does not promote. https://www.chessvariants.com/piececlopedia.dir/dragon.html

Mirror: it moves like a pawn but it can steal the way another piece moves or does stuff by eating it

Voyager

The Voyager plays like any piece (allied or enemy) adjacent to it.
To put it precisely, it inherits normal movement and capture abilities from any piece that is orthogonally or diagonally adjacent to it, until it separates from that piece.

Till here, this is like the Mosquito in Hive. Surprisingly, I haven't been able to find a chess variant piece with this ability.

But the Voyager is capable of more.
- In one single turn it can do a series of multiple moves, each time again copying normal movement and capture abilities from a piece that is at that point adjacent.
- During that series it can only capture one enemy piece. But after this capture it can proceed to move further without capture.

Example:

White to move, during white's turn the Voyager can:
- move as Knight from c3 to d5, continue as Bishop to h1, continue as Rook to h6, continue as Guard (or Queen) to take the Queen, continue as Knight to go to f5, continue as Bishop to go to safety on c2.

The Voyager must imitate an adjacent piece like it is of its own colour. This addition is important when, e.g., a Voyager is imitating a pawn: when a white Voyager is adjacent to a black pawn and takes that movement, the white Voyager must imitate a white pawn and not a black pawn.

An isolated Voyager (having no adjacent pieces) cannot move or capture.

The Voyager is a route exploring piece. I had tried something like that here.

The post numbers have been messed up with after some time, can you find it again and post the link?

The Pusher:

It moves like a king, but it can move into a royal piece and when it does then the royal piece is pushed in the direction of the pusher. Great for converting light sqared bishops into dark squared ones and vice versa.