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Pawn's promotions are part of the standard FIDE's chess rules, so they also apply after a swap that places a pawn in the last rank of the board. A pawn promotion is actually an extra move or action that follows a normal move of a pawn.

That is not a logical conclusion. FIDE rules don't allow swapping pieces, and whether you chose to consider a swap as a normal Pawn move with an extra action or consider it a normal move of the piece the Pawn was swapped with, with an extra action is your personal choice, which the reader cannot know unless you mention it in the rules. Whether a Pawn that returns to 2nd rank has a double push depends on which of the equivalent formulations of FIDE rules one uses (i.e. whether a Pawn that never moved before has this move, or any Pawn that is on 2nd rank no matter whether it moved or not, or whether any Pawn that is on its own board half can move up to the mid-line.) The rule description remains completely inadequat.

It is also not clear how promotion affects the set of 'outer pieces', and whether capturing a piece resulting from a promotion adds that piece to the set, or just a Pawn.

And of course I am still of the opinion that your 3 submissions are too similar, and should all be presented in a single article.