Cerebellum Segmentation

I import the surface file (right-click on subject > Import surface > Select: atl-Buckner17_space-MNI_dseg.nii).
My question is: How does brainstorm take a volume parcellation atlas (.nii file) and projects it on the surface? Is it a reliable method?

There is no "Projection on the surface".
This menu "Import surface" applied to a volume parcellation creates a new surface file which includes the tesselation of each parcel (computed with Matlab isosurface function).
The output of such procedure, beyond visualization, is very limited.

Also, when I import the Buckner17 Atlas, brainstorm splits the scouts in right and left direction. For example scout 2 is split into scout 2 R and 2 L. How can I neglect this split and keep the original atlas' scouts?

What you get here are not really scouts, but actual surfaces... it does not make much sense to merge them.
If you want to use the parcels from your atlas as scouts in the context of a source analysis, then the best solution is maybe to use a volume source model and load the atlas a volume atlas:
https://neuroimage.usc.edu/brainstorm/Tutorials/TutVolSource#Volume_atlases