A, B are nothing.
D is a balk (or ball with no one on base)
C should probably be play on, but depending on the wording of the rule in the particular ruleset you are using (you didn't say which) regarding detached equipment, I can see some umpires awarding bases here.
I wouldn't. I believe that the INTENT of the detached equipment it to prevent INTENTIONAL striking of the ball with said equipment, and in this case, it's the ball striking the equipment, and no intent exists.
I expect some here may disagree. I would probably rule play on.
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"Many baseball fans look upon an umpire as a sort of necessary evil to the luxury of baseball, like the odor that follows an automobile." - Hall of Fame Pitcher Christy Mathewson
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