The Pen on the card on the bottle is the same idea. The difference is the pen is long and the bottle opening is small. Thus a small tilt (caused by friction between the card and pen as the pen is flicked) may cause the pen to miss the opening as it falls.
With the stack of coins, if the bottom most coin is struck quickly enough by the ruler, the frictional forces between this coin as those resting on top of it, can not act long enough to tilt the stack. Thus the stack's inertia tends to keep it at rest, and, once the bottom coin is gone, the rest of the stack falls straight down without falling over.
As the strings hang with no one pulling on them, there is tension in the upper string due to the hanging mass.
If the lower string is pulled quickly enough, the large mass's inertia will tend to keep it in place and the tension in the upper string does not increase enough to break the upper string. If the lower stirng is pulled slowly then the tension in the upper string increases and is greater than the lower string because the upper string is being pulled by the lower string and it is holding up the mass. Thus the first string to break should be the lower string.
A large mass hangs freely in a pot. The pot rests on a table. If the table is struck, the table will move the pot and since the mass tends to stay at rest, there will be relative motion between the pot and mass. The motion will not be great, but one can attach a straw to the large mass and the end of the straw will move a noticable amount. The initial relative motion will cause the mass to wiggle. So, one will see the straw wiggle. In motion sensors, something is used to damp these oscillations, such as a fluid.