If you are comparing gas to heat pump efficiency, it is more like 85-90% vs 350-500% efficiency.
Because in the gas furnace efficiency they only calculate the efficiency of burning gas but miss to include the auxiliary electricity that is needed to run the system.
In a heat pump system everything (running fans etc.) is included in the efficiency calculation. The efficiency itself is depending on the source of the heat pump. In a really harsh climate a ground / geo thermal source might make sense. But usually the average temperature is higher than you might think.
And for the environmental effect: modern gas power plants run at 50-60% efficiency so with a heat pump you are always burning less gas even if the gas plant is less efficient then the gas furnace.
It would be interesting to know what extreme cold means.
Sure it can. Battery state, temperature and all is controlled by software…