If you know what I do, you can make your own.
Fridge, you can make an evaporate cooler wherever there is a breeze (or a breeze funneled into the back of it, or a solar fan fitted) they are just the box which is the fridge, a towel over the top and water is tossed on it now and then, with a cup or a solar powered timer and pump if you want super fancy. These things work extremely well. Everyone should have one for drinks on hot day.
Cooker, probably a rocket stove is good, turns twigs into hot pots and is easy to make.
You'll also want a hot box to do the cooking once the pot is hot, it saves a lot of fuel.
Solar cooker for when the sun shines.
There is a suspicious shortage of washing machines for camper vans, probably because any container that you can seal up with water and clothes and put in the boot of the car is a washing machine when you drive around. Can't be hard to make a container holder with a cranking handle like they draw prizes from for home use.
Everyone should build their own solar water heater, they are too easy, cheap and effective not to. I have 300 + litres of scalding hot water 24/7 and I built it from trash.
Mr Tesolonian builds an evaporate cooling door of all things, but there are plenty of other ways to make them.
Oh mr Tesolonian also shows you how to run petrol engines on wood, but that's another story.
Can't think of any more appliances.