Q: Can the battery back up really run the heat pumps and for how long?

A: A 10kWh battery can only power a heat pump for an hour or less. The better way to add a battery is to keep your fossil-fuel furnace and have the battery run only the emergency circuits on your house like the fridge, lights, burner circuit, circulating fans, water pump and a few outlets. Together these might draw about 10 amps, 1kW or about 1 kWh per hour so a 10kWh battery would last you 10 hours.