Right. And with the current scale of infrastructure that's used, financing models, market incentives, and cost of fuel, the current density required mostly only occurs in the downtown core of cities, or in industrial parks near a power station (where the waste heat from power generation can be used to heat industrial processes like refining petroleum or cook paper pulp - sometimes this is called "co-generation"). But that's not to say it's a bad idea! You would just need to move the needle on any of those things in the list - for example, making denser homes around a lower cost heat source like a ground sources heat pump powered by solar.

No. Two houses connected to each other can already save money and energy by means of sharing one larger/better installation instead of two "small" ones.

Can they? Aren't most modern heaters (oil, gas) close to 100% efficient? If you get an extra percent or two out of a larger system I'd expect that to be lost in transmission between the heater shed and the house.