Does running the pool heater at night save money?

No it doesn't, Night time heatloss is a big problem for pool heaters, as your pool pump runs it moves heat away from your pool, so you actually increase the night time heat loss by running your pool pump/heater at night. The most economical solution is using a Solar cover and leaving your pump off at night to prevent night time heatloss and then just fire up your heater when the temperatures begin to come back up to daytime levels.