For the first method, you need to loop through all instances and set their instance variables to false before setting the current one's instance variable to true. You should use subevents, not separate events, so that things happen in the correct order.
The second method should not use an instance variable at all, but a local variable. On clicking any CheckerPiece_Red, you should set a local variable (defined ahead of time) to that instance's UID or IID. This way you don't need to deselect any previous pieces, as there can only be one active piece.