Datasets will be spawned as GameObjects, with a VolumeRenderedObject component attached to them.
You can move, rotate and scale these objects like any other GameObject in the Unity Editor.
Spawned datasets can be saved as a part of the scene (simply save the scene).
However, if the datasets are large (or many) this will cause the scene asset to become very large, and saving/loading will be slow (or crash!). To prevent this, you may consider importing your datasets as an Asset (see import documentation) and referencing the already imported dataset through some script and spawning it through the VolumeObjectFactory.
To change the appearance settings and other volume rendering related settings, see the appearance settings documentation.