Thank you for all these explanations and feedbacks. I will correct soon the description on my own page.
The end-o-game rules, checkmate, stalemate, etc. are identical to standard chess
King's jump: you guessed well. At his first move, the King may jump to a free square at 2 squares' distance. It does not matter if the square jumped over is occupied or not; however, the jump os forbidden if that intermediate square is threatened by an enemy piece. When jumping like a Knight, at least one of the two intermediate squares must be free of threat. The King's jump is not permitted if the King is in check.
The King cannot capture with its initial jumping moves (it may jump to a free square only)
En passant: any time a Pawn or a Prince takes a double step and passes through the capture square of an opposing Pawn, that Pawn may capture the Pawn or the Prince as if it had only moved one square. This en passant capture must be made in the immediate move following the double step. Only a Pawn may capture en passant; the Prince does not have this option.
Thank you for all these explanations and feedbacks. I will correct soon the description on my own page.