1. Delta-T Makes the World Go Round:
Any time the temperature in a room(s) is lowered, the differential temperature between that room and the colder outside temperature lowers. Heat transfer is based on this delta-T, so the warmer your room is, the more heat you're losing, regardless of level of insulation.
It is absolutely more efficient to lower the temperature for as long as you can, any time you're able to. The argument that keeping a room at a constant (high) temperature appears to use less energy is 100% false.
2. Many furnaces work much more efficiently when they're allowed to run for longer, less often. My old condo had a programmable thermostat that was programmed with the minimum temperature on/off setting / droop. I believe it ran every 15 minutes or so when it got really cold out. When I checked the housing of the old furnace, it was cold to the touch.
I changed the on/off/droop setting to max soon after moving in (4F, IIRC). When the furnace ran or longer, it ran hotter and transferred more energy through the vents. This does mean that more heat was lost through the ducting, but the ducting was all in the center of the house, so it wasn't a total net loss.
The main benefit, I believe, is less heat cycling of the furnace heat exchanger. Instead of going from cold to hot to cold every 15 minutes, it would stay off for longer, then burn for longer to makeup that 4F, letting the heat exchanger to reach its max temp and stay there until it turned off again.