Maybe gently for 'schonend'?
Due care sounds to me like legalese.
Treat is better for objects that can be picked up and moved but that don't have moving parts, like furniture. Treating something gently means taking extra care not to damage it or strain it, put it under undue stress.
You can also handle something gently or with care, but mainly for smaller, more fragile objects, such as china or glassware, bric-a-brac, etc.
Maintain would be more for something with more complex parts that perform more functions: buildings, vehicles, machines, appliances. It means not just passively avoiding damage, but actively performing regular maintenance, doing whatever is necessary to keep something in good condition. If you used that word for furniture, it would mean doing something to it more actively, like waxing or polishing it. And you would just say 'maintain it in good condition,' you wouldn't use a word like gently or with care.