PNP pull-down circuit
I believed that closing the S3 switch (after the C1 was fully charged) the PNP transistor instantaneously would discharged the C1 capacitor.

The transistor is not a perfect conductor. It has some &quot;resistance&quot; (although it is not linear i.e. it doesn't obey Ohm's law). That resistance keeps the capacitor for discharging instantaneously.

Instead the discharging time is affected by R1 value

Yes, the current through the transistor is roughly regulated by the current through the transistor's base. The smaller the base resistor, the more current will flow through the transistor. Typically, somewhere in the neighborhood of 50-200 times more current will flow through the collector than through the base. However, that number drops when the transistor is &quot;saturated&quot;.