Yes, they are typically calculated as having above 100% efficiency as they use the energy to move and concentrate heat instead of producing it like other heating systems. I agree that this is technically wrong, but it does make sense when looking at it in the above context of heating systems.

Yes, over 100% efficiency is exactly what I claimed. In winter, you'll get more BTUs of heat output from a heat pump than you had put in as BTUs of electricity input -- because instead of converting the electricity to heat, it's using the electricity to pull heat from the outside and put it in your house. Hence, it's a more energy-efficient way to do things than the laws of physics would allow for a device that directly converted electricity to heat. That's what it means to be a reversible air conditioner, yes.

IDK why me saying that is some kind of controversial statement -- it's simply a factual description of the product. There are scenarios and real-world constraints which may mean it's more or less sensible to install one, but over 100% efficiency is, exactly, the selling point of a heat pump.

Yes, he pumps do move more heat than the electricity that they consume. That's because they are a heat pump, not an energy conversion system like a motor.

No it doesn't - you're not creating heat, you're moving it. You can move more heat than the amount of energy you expend moving it. Hence the efficiency above 100%

It's a really bad piece of jargon, but is an internally consistent definition. They mean (heat entering building)/(work consumed) > 1

Which is a way if defining efficiency (energy out / energy in), just a really awful and misleading one.

In terms of % of carnot efficiency, the best heat pumps are about where stationary heat engines generally are, 40% or so.