Why are Pins 7 and 5 floating for this 555 IC and how does an NPN and PNP transistor when connected to E B C act a switch? Without the use of Pin 7 surely the capacitor cannot discharge which would render it useless?
Capacitor connected to pins six and two is charged and discharged by the output pin 3.
That is a common charge/discharge method for producing a 50% duty cycle.
Pin 5 can be left open like it is. Normally a capacitor is connected from pin 5 to ground. Pin 5 is the control voltage reference for pins 2 and 6. So a bypass capacitor might be needed for better stable reference voltage.