Sure it can. Battery state, temperature and all is controlled by software…

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.

I hope this is a serious question, obviously this depends on your baseline. In 2013 Germany had a 56% share of fossil fuels, 27% share of renewables and 17% share of nuclear power generation. In the current year, the shares are: 59% renewables, 39% fossil fuels and 2% nuclear power generation. So in the last ten years there has been a switch in generation from both nuclear and fossil fuels to renewable generation. Could it have been better in the wake of the looming crisis of both climate and energy? Yes, I think it would have been better to keep some newer nuclear power plants running. But Cpt. Hindsight always has it easier.

In the long run every successful economy will generate its major share of electricity from renewables. Some countries will choose to generate a part with nuclear, others will choose to use a mix of hydrogen, batteries etc. to complement renewables. We will see what works best.

While in hindsight not all the decisions of the German energy policies seem right and it would have been better to keep the nuclear power plants operating for a few years, there was never the plan to replace nuclear with coal. All of the nuclear power generation has been replaced by wind and solar power generation. In fact, the plan was to phase out nuclear and replace the remaining coal generation with natural gas power plants. This definitely got more difficult in the time of LNG. The plan in any case is to phase out coal as well and with 56% renewable generation in 2023 Germany is on track to do so.

Ofc there is a xkcd for this… Great thing is that I did not know this one yet, so thanks!