Sorry that I wasn't that clear, I meant the Cannon moves like a king, but it launches pieces like a rook. Also, the Cannon can only launch pieces in the direction the piece is to the Cannon. As in the example, the pawn on c4 gets launched to g4, but it can't get launched in any other direction i.e the b file or a4
New Fairy Chess Piece: Cannon
Pawn promotion by the cannon can only happen when the entire file is clear which only occurs in the end game, using a rook to guard would do the same thing, just a lot slower. If the enemy team has a piece guarding the back rank, that pawn can be easily captured. If you still don't like the cannon, just like the Grasshopper and Amazon, you don't need to include the cannon in every game.
And if a pawn gets launched to it's home rank or further, the pawn regains its double step move option.
Yes, but only if it's a capture. Like getting fired blows up the piece, disincentivising it. Also, can the cannon do normal king captures?
Yes

The Cannon moves like a King, but if there is a piece orthogonally adjacent to it, the Cannon can launch it like a rook. The piece gets launched to the other side of the board, but if there is any enemy piece in the way, the launched piece lands on top of it. It lands behind any same colored or team piece.
Example:
(Pretend the Chariot is a Cannon) The cannon on b4 can launch the pawn on c4 onto the bishop on g4.