Kitchen ranges, clothes dryers, and literally every other appliance large or small are usually moved with the homeowner or tenant in Germany - until the last decade or so, rental apartments almost always came with completely empty kitchens, and it was on the tenant to fit in the cabinets, appliances and even the sink. Bathroom cabinets are also usually the responsibility of the tenant, but the toilets, sinks, and showers/tubs are built in.

On the upside, even a small studio apartment usually has enough space and an extra water hookup for at least a washing machine, so no dealing with other apartment residents or a public laundromat for laundry. Dryers are usually condensing; no need for an outside vent.

Until the last few years, short tenancies were unusual for Germans; in the little building we rented in before we bought our house, the other tenants had been renting there for 20-40 years! Given the terms of our contract, I gathered that they must have had very small, if any, rent increases written into their unrestricted contracts, and the only way to get them out was if the building owner decided to live in one of the units herself.

Sometimes yes. Often they stay, especially if they are reasonably new and the buyer wants them. It's seen as a selling point that the buyer won't have to go out and buy appliances right away. Of course the hidden downside is that they are financing used appliances for 30 years so it's generally better if the buyer negotiates a lower price in lieu of appliances. But a lot of new homebuyers don't think about that.

But I'll grant that appliances are probably moved more often than water heaters are.