it was not easy to regulate
I think Louis is right, that sure does look like the minis which AEG sold way back when.
The dryers are definitely Cordes, that drum, that boot, that lip in the upper panel is all Cordes - Siemens could never be bothered to achieve that level of quality themselves (they are about the only European white goods maker whose quality got better over the last 20 years. And it needed to.)
The coal fired water heater was an open tank. This means water was only then displaced when a valve let cold water in. Once you began the heating, there was no way to stop it. You heated about 40 gallons of water to more or less near boiling (took surprisingly little coal) and it heated the whole bathroom along with it. I found the warmth very pleasant, it was very much radiant heat. The water, of course, was enough for very long showers or a full bath of very hot water or two warm baths.
They were very common after the war, burnt most solid fuels - coal prefered - and in the late 70's were gradually converted to gas burning, just like the coal fired gravity furnaces in the 'States.
Nowadays, Europeans tend to use demand water heaters. Running three phase at 7, 8 or more Kilowatts they put out very hot water with high effeciency...but are only about 16 inches high by 12 inches wide by 4 inches deep. Waterproofed, they are usually hung right about the bathtup. Work great, but eat electricty like mad.
The old water heaters used to run dry occasionally. The soldered joints would melt (molten lead in the bathroom, delicious) or, even more fun...people might let them run dry then add cold water to the red hot metal.
Dangerous and unsafe at any speed.
What it comes down to is this. Until very, very recently, Germans (most Europeans) did not have hot water or gas or high voltage electrical lines in their bathrooms. The English still have a lot of really archaic rules, which even the continental Europeans have given up.
This lead to lots of self-heating appliances. Since a slow rise in temperature over a long time is the ideal way for enzymes to dissolve dirt, enzymatic detergents became much more popular here than ever in the 'States. Properly rinsed, they are also easier on the skin, too.
I think US homes were more comfortable until about the late 1970's, then the Western Europeans caught up and moved far past. Pity, but as soon as a country decides it is the best, most advanced and perfect place in the world...well, look at Japan until the 1870's...