#11 No there aren't. The number of possible chess positions is countable (similar to http://jdh.hamkins.org/game-values-in-infinite-chess/ ) and finite, and the number of positions you describe is less than that number.
#13 #17 There doesn't need to be a forced win, just a possible win. See comment #3; every chess site allows even a pawn to mate regardless how unlikely the pawn is to win. Ditto for other piece configurations, provided that a win is possible.
#13 #17 There doesn't need to be a forced win, just a possible win. See comment #3; every chess site allows even a pawn to mate regardless how unlikely the pawn is to win. Ditto for other piece configurations, provided that a win is possible.