When I append a landing platform that I animated and added object constraints to (child of) into a new file everything is there from textures, keyframes to object constraints, but when select everything to scale and move it according to my new landscape, the animation doesn't work properly anymore. The moving parts skip to other locations and move far away after scaling it all down. Is that a parenting problem or how can I make sure that it still functions after scaling and moving it around in a new file?
You can try to use Copy Location, Copy Rotation, Copy Scale constraints. These constraints can be set to local space, so that only local transforms will be taken into account.
You can also choose the root thing (for example root bone) and set a custom space using this object:
The problem with keyframed animations is, the values stored in their keyframes are usually local values, always in relation to the parent object or if unparented, relative to the world origin.
Let's say you create Earth and Moon, and the Moon is orbiting around the Earth. If the Moon is a child of the Earth, you can move the Earth around and also scale it, and the Moon will keep orbiting the Earth and its size and orbit diameter will be scaled relative to the Earth's scale.
The problem is: this only works if the Moon is a child. If they are both unrelated objects, even if you select them both and move and scale them to a mutual pivot point, Earth and Moon will keep the new scale, but the Moon's movement is determined by the location coordinates stored in the keyframes - and they are relative to the world origin, if the Moon is not a child of the Earth.
The same goes for all your objects. If there are objects not parented to anything like this landscape you mentioned or have Child of constraints targeted to this landscape, then moving and scaling them will not make their animations relative to the landscape.
In this case it might be better to not move and scale all objects to the new landscape, but place/move and scale the landscape according to the animated objects. Then either parent all objects (that are not already children of other objects) to the landscape or those objects and the landscape to an Empty, and afterwards moving and scaling the Empty (or the landscape, whatever you make the "top level parent") to the desired location and size.