Capacitor behavior and construction confusion

Question

I’m trying to better understand how capacitors work. From my understanding, once fully charged, a capacitor stops the current flow, but I find this confusing since it seems like the design should allow continuous electrical flow. Is there something in the circuit that’s not shown in standard diagrams?

Also, looking at the internal structure, both the positive and negative sides of a capacitor seem identical. What causes an incorrect connection to result in failure or even an explosion?

In: Engineering