Can I use this sign for a labor strike?
No, this specific sign is used for a penalty, demerit, or a 'strike' against someone's record. A labor strike uses a completely different sign, typically involving an 'S' handshape twisting near the side of the head.
Is this the same sign used for a strike in baseball?
While it can conceptually mean a strike in a game, baseball umpires and fans typically use the traditional umpire gesture—throwing a fist up and back—to indicate a called strike in baseball.
Does it matter how hard I tap my elbow?
A firm, deliberate tap is best. You do not need to hit your elbow hard enough to hurt, but the motion should be clear, crisp, and intentional to convey the idea of a penalty being officially recorded.