I have to check but fridge should not be an issue. They are practically battery power capable nowdays.
A couple of years ago I was looking at what existed in refrigerators that you could carry in a car. The only options were thermoelectric wimps--they are only good for 40 degrees of differential and aren't capable of much more than keeping themselves cool--it takes ages to cool down something warm you put in them. Lots of power draw, though.
A/C could be an issue but I suspect you live in poorly insulated house where everything is pretty much open all the time.
With properly insulated house you will not have much problem with solar powered A/C.
Again, I think you underestimate the problem. Around here the code requires pretty good insulation. IIRC we have R-38 in the ceiling and R-19 in the walls, dual-pane windows. That still adds up to over $250 in power for cooling in the hottest month.
And that also is a problem for your nighttime power numbers. Here in the hottest months it's not unusual for the AC to be needed even in the middle of the night.
And electric water heater in Australia? are you insane? Last time I checked you had sun every day.
And again, I suggested nation wide grid for clouds.
Lets look at the economics of it some more.
1) In climates where it does not freeze you can use a direct loop solar system. My parents lived in such a climate, it worked well. Here, though, the winter nights are a bit cooler. Keeping a direct loop system from freezing is not very practical. Thus you're forced to use systems with a secondary coolant loop--and now the system is about 4x the price. I don't exactly like such systems, either--what if there's a leak between the coolant and the water?
2) Not everyone has a suitable place for the collectors.