Smallest possible 2D and 3D chess

Smallest possible chess variant probably must have only 1 square. But it's 0-dimensional game. If it have 2 squares, it's 1-dimensional game. These variants are not invented yet (there is game "Bushi shogi", played on 2 squares, but it don't look like chess. It have several common things with other 2 extremely small shogi variants by same author, but not with other chess variants), but i hope, they will be invented. Smallest possible 2-dimensional variants have 3 squares, smallest possible 3-dimensional variants have 4 squares. And they are already invented! And until these 1 and 2 squares are variants will be invented, they are smallest chess variant in the world!

Setup

3-square 2D board and 4-square 3D board are quite similar.
2D board is 2x2, one of cells is removed:

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square 1 is white player's home square, square 3 is black player's home square. squares 1 and 3 are white-colored, square 2 is black-colored.

3D board is same, but there is square 4 (white) directly above square 2.

Board, of course, starts blank. Each player have 4 pawns, 1 king, 1 queen, 1 rook and 1 bishop in hand (see "rules"). Knight and unicorn are not possible on such board.

Pieces

All pieces, expect pawns, moves just like in standart chess. On these boards (both 2D and 3D) their moves may be described in this way:
King and queen can go to any square from any square.
If bishop is on white square, it can go to any other white square, on black square (square 2) it cannot move.
From square 2 (black square) rook can go to any other square, but on other squares it only go to square 2.
Pawns are a little more  complicated. Remember that it still moves without capturin orthogonally, captures diagonally.
From home square it can move without capturing to square 2, can capture on opponent's home square and square 4 (if it's 3D board). From square 2 it can move without capturing to opponent's home square or to square 4, can't capture. From square 4 it can move without capturing to square 2, can capture on opponent's home square. It promotes to rook, bishop or queen on opponent's home square.

Rules

In beginning, all pieces can only be dropped to home square if empty. But all non-pawn pieces may be off-board promoted, it will give them more dropping options (if you'll decide to play this game with physical board or Game courier, you can mark off-board promotion by moving piece on board area, wich is not used in game. This, of course, will make you feel this game as played only on 3 or 4 squares lesser). When piece is off-board promoted first time, it can be dropped to any empty square. When it is off-board promoted second time, it can capture with drop.
Instead making normal move, it's possible to remove any friendly piece from board back to reserve. If it was off-board promoted, it demotes back (remember that pawn promotion is different from from off-board promotion, and thus, promoted pawn will never become pawn again!).
I did not chosen, wich winning conditions are better, and you have to chose before playing:
1. Win by stalemating opponent. Checkmate is impossible.
2. King can't be removed from board to reserve when in check. Win by checkmating or stalemating opponent.
3. King can't be removed from board to reserve when in check, unless it's check by piece out of board. Win by checkmating or stalemating opponent.
4. It's not allowed to remove pieces at all. Win by checkmating or stalemating.

You may also chose rules, similar to 2 or 3, but stalemate is draw or win for player, who is stalemated.

Here are some other possible variants:

2 ways of off-board promotion: non-pawn piece in reserve can be promoted in 2 ways: first off-board promotion may be same as in original variant, or piece may become able to capture on home-square by drop. Second off-board promotion is same as in original game.

Pawns also may be off-board promoted, but it can't be dropped to opponent's home square.

Square 4 is not directly above square 2, but above empty space of first level.
Bird's eye view (square 4 is higher than other squares):
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Unicorn (piece, wich move triagonally, see Raumschach) is possible.

As pieces have no opening positions, it's possible to play with more pieces of more kinds. Here are some ideas:
Demoter. Can be dropped only to home square, moves as non-capturing pawn. When it reaches opponent's home square, it is removed from play and one of off-board promoted pieces (demoter's owner to choose) demotes one level back, and pieces, wich are not off-board promoted (but able to promote) may be captured.
Berolina pawn. Moves as normal pawn captures, captures as normal pawn moves. Have same properties as normal pawn.
Shogi pawn. Have orthogonal moves (capturing or not) of 2 other kinds of pawns.
Stone general/crab (moves and captures diagonally forward) is also possible, but not recommended.
Crooked rook. Moves rook, but may make turn 90 degrees and make another one step. Maybe, it worth to replace normal rook with it.
Lance. Hybrid of shogi pawn and crooked rook. Moves as shogi pawn, but may make second step (if first is non-capturing, of course). Have same preperties as pawn pieces.
Cannon. Moves without capturing as crooked rook, but to capture, intermediate square must be occuppied. Korean variant is possible, but it would be simple weaker bishop.
Immobilizer. Moves as crooked rook, but don't capture. On home suare it freezes piecd on square 2, on square 2 freezes piece on opponent's home square, on op. home square freezes piece on home square if board is 2D or on square 4 if board is 3D, on square 4 freezes home square pieces (it's only example, you can use another sequence). Frozen pieces cannot be moved back to reserve. Suicide capture (see Ultima) is optional.
Orthogonal draught king. Moves as rook, to capture must move 2 squares as crooked rook, captures piece on square 2 (can capture only on 1 square! Probabbly, too weak).
Let's discuss special pieces for alternative unicorn board. Rook-bishop compound will be different from rook-bishop-unicorn compound (2 different kings are possible to). Plus, bishop-unicorn and rook-unicorn are possible.
I'll add other piees later. New ideas are welcome!

Notes

I played it once, but still not sure that it's playable enough, but i think that it is playable: original variant have 12 opening moves. If played with pawn off-board promotion, 13 opening moves. 2-ways off-board promotion, there are 16 opening moves. If played with both, it have 18 opening moves (almost same number, as in orthodox chess!).