In terms of the tank, you are correct that capacity for a full tank is 80%. However, you need to call the propane company to come fill the tank at ~20%, because you don't know their delivery schedule. This is typical regardless of use case. So you have a real usage capacity of less than 80% and more like 60%. BTW, you want a large tank for multiple reasons, not just run capacity.

20kw generators are fairly standard for whole household. Many people have even larger. You are right, they are not going to run them full tilt for 24 hrs straight. That's why I said 2g/hr which is in on the low side of typical 1.5-3.0 g/hr range. You want your generator load to be in the 30-50% range for efficiency and longevity. I fully expect a full 500g tank to last more than a week typically, but we really don't know the use case here. So you have to use the numbers off the data sheet. Otherwise, you are under sizing. At least with the 500g tank you can go an entire week typically and you don't have to worry about it not.

In terms of batteries, you go ahead and use those batteries in zero temps. As I said there are some which can be used down to -4f, but beyond that they can't be used. Those batteries also aren't being widely used for household power. BTW, standard lifepo4 does not make any significant heat being discharged or charged. That's one of the beauties of that chemistry over lead acid. Sounds like you are quoting marketing for EV use. At least you acknowledge that you need to heat the batteries. There's plenty of horror stories where people put lifepo4 in camps, garages, out buildings, etc and heat failed and the batteries were bricked. You can just google it.