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From the chair of the co-exec to Grenv (but to be ratified by the inventor) ...
1. We will need to think about this one. Initial thoughts are that the King can impost another piece to get out of check so long as the King leaves the checked square and lands on an unchecked square without crossing another square which is also checked, a little like not being able to castle. Knight moves may be made with only the landing square required to be not checked.
2. No, as the pawn double square move is the first move that a pawn makes, for the King to get to the second ran he must already have moved.
3. No, as the impost move is only to get out of check not for placing a check.