Once again, you are making progress - and that's good.
The difficulties you're having is not from a lack of information but result from not yet fully intergrating the information you already have. You are still laboring under a few (but important) misconceptions.
One minor thing I noticed in passing is that you aren't aware of window-sized heat pumps. I don't know where you live but they are VERY common in parts of the country in apartments and condos. The reason is that they provide both heating and cooling from the same unit and avois the complexities of providing furnaces in individual living quarters. It also saves the time and effort of installing electric resistance heaters along baseboards, though that is still quite popular too.
But since air conditioning is required anyway, you simply buy ONE unit, stick it in a window, plug it in and you immediately have both heating and coolilng. "Extra parts???" The only difference between just an air conditioner and a heat pump is a 4-way valve and a couple of short lengths of copper tubing.
Sure, heat of vaporization is the key to
any refrigeration system!! The reason you didn't see it mentioned anywhere is because it is so
elemental that all the writers assume that everyone already knows that. (It's about as basic a principle as you can find.)
The following two statements of yours clearly show that you still do not completely understand the refrigeration process even though you make every attempt to claim that you do:
"I would bet that the heat pump scheme cannot work at all with a working fluid that does not exist as a liquid part of the time and a vapor part of the time."
And, "On the other end, when the Freon expands, it becomes colder. Droplets form because the freon got colder, which is a mixed advantage and disadvantage because this reduces the pressure, making the gaseous portion even colder, but the droplets release heat, which makes things warmer again."
Of course it won't work without being a liquid at times and a vapor at other times. That IS what allows it to use the heat of vaporization. Unless there is that phase change, the device is useless.
Yes, as the freon expands it get colder (another basic principle) but NO droplets form in the evaporator where this expansion is taking place. It enters the evaporator
already in a liquid state through an expansion valve or capillary tube (which is simply a very small diameter piece of tubing) and there it does nothing but evaporate - turns into a gas. There is NO condensation taking place which releases heat - none.
The only place condensation takes place is in the condenser (thus it's name) and that's all the way over on the other side of the process.
Seriously, once you get past these few little things you'll have a reasonably good understanding of the subject.
