This is from the Top Score (2 player version of 300) schematic so it may not be exactly right for 300:
1) The A/Alternating relay is activated by the KS/Advance Unit relay which is one of those very small AS style steppers.
2) The right side target lights are controlled by the EX/2nd or 4th Ball relay. The left side target is always on. All targets also go off briefly as the score motor turns.
3) The capacitor, along with a diode and resistor are part of the delay module, typically mounted on a jones plug, to delay the firing of the I/Add Bonus Delay relay. These are used for example to let a spinner stop spinning before awarding points selected by the spinner.