Very very low chances. But this is more about covering one's ass (avoiding liability altogether) instead of doing proper plumbing work and estimating failure probabilities.
You are more likely to puncture a pipe nailing a picture to the wall or putting down carpet.
It's amazing in Germany everybody installs their own kitchens in rental flats, which they move from flat to flat, plus their own washing machines without issues.
Installing a washing machine? As in the no tools required pipe from the wall, the other pipe to the wall and finding a socket somewhere? I'm amazed people pay plumbers to do it!
For OP as long as they're sensible it should be completely fine, just don't do what I did and forget to put the drain hose in the sink.
As for the comparison to Germany, if you install or get installed appliances yourself, I'm sure you you yourself would be liable for any damages. If the landlord has fitted an appliance for you then more likely the landlord would be liable for damage from leaks.
In an old house washing machines and such like might not be desired because of noise.
They then asked the landlord to install a dishwasher.
Or the landlord needs to, which costs money --> they don't want to do it.
I still find it hard to believe a dishwasher (for a couple) will cause a 50% difference in water consumption.
The landlord will also have a liability insurance, which will cover him for all damage to the external part of the building, plus any claims made by the tenant if for example, a badly fitted window blows open and hits the tenant.
As for a dishwasher as you describe, no need to ask for permission and just take it with you when you leave.
I don't understand why tenants should be forced to have insurance for an appliance installed and fitted by the landlord. e.g. in case a dishwasher springs a leak and damages the property.
If for any reason the tenant took it upon himself to fit an appliance, and it caused damage, then it would be down to the tenant to pay - hence the insurance.
Exactly my point. i.e. a reason why a landlord would not install one themselves.
He/she means back-filling from the drainage hose. If it's not in some place higher than the water level in the sink then the contents of the sink can drain into the dishwasher - the u-bend isn't high enough. Usually just needs tying up close to the top of the sink.
And that's different to back-flowing down the feed pipes which can happen if there's work in the house and the water supply pipes are drained. Theoretically water that's in the appliance, including contaminated water, could get sucked into the supply pipes and would come out potentially through someone else's kitchen or bathroom tap etc. when things are connected back up. Not really what you want. It's unlikely but obviously does happen hence the requirement in some places/cases to have a non-return valve.
Unless she is lazy to read or interpret a simple diagram, she will have all the data to have an informative decision.
You will make everything clear and transparent, and avoid to have to explain any other issues if she sees the counter-top dishwasher during a visit to your apartment for any other reason. As you said, she is troublesome and will implicate with you if you communicate or not, than better to try to communicate.