You’ve found a bug! (result of some recent code refactoring) When you selected the rigid preset, it got reverted to the default preset because the two presets had the same ID. The issue is now fixed, update SlicerElastix extension to get the updated version of the extension (only on latest Slicer Stable Release or very latest Slicer Preview Release).
It is up to each library and application to decide how to organize the voxels in memory and assign IJK coordinates to voxels. However, medical imaging file formats unambiguously specify where the voxels are in physical space. Therefore specifying transformation in voxel space is not an option, but registration methods must always provide transformation in physical space.
You have access to all information (most notably the computed transform) and you can do anything with it (save to ITK transform file, use it to resample the moving image, warp segmentations, models, markups with the transform, etc. each by a few lines of Python script). You can find examples in the Slicer script repository, in Slicer forum posts, tests, and examples, which you can find using Google, you can often get fully functional Python code by asking Bing chat, and you can of course also ask specific questions here from us.