_If a capacitor is needed across the latch pin (and if so, what size).
No that was a mistake in the original tutorial. There should be a 0.1 ceramic capacitor on the 5V and ground of each shift chip.
You don't need a seriese resistor for FETs as you have drawn but your text says you are using a TIP122 that is not a FET and you will need a 1K seriese resistor.