at what temperature does a air source heat pump use as much energy as it produces?

Answer 1

The energy balance over a heat pump is:

Heat into evaporator from air + Heat in compressor = Heat produced from condensor

The air has to be hotter than the evaporation temperature of the refrigerant at the prevailing evaporator pressure. This temperature will depend on the type of refrigerant used. Compressor protection devices will shut the unit down if the air temperature gets too low for sufficient evaporation. However even at low efficiencies the unit is always producing more energy than it consumes (see energy balance).