To keep things simple, make the segment cover the region you are interested in. Then, you can us Mask volume effect to blank out the parts outside your region of interest.
Yes, this is correct. All effects (Scissors, Surface cut, Paint, etc.) only modify segments. They will not modify any volume nodes.
If you blank out a region of a volume, Elastix will still take those voxels into account. This is probably not what you want.
To make Elastix ignore certain regions then you can specify masks in “Masking” section in “General registration (Elastix)” module. You can create a mask volume by using “Fill inside and outside” option in Mask volume effect.