what is actually happening alignment wise when symmetry is imposed.
In general, nothing is changed during alignment. Symmetry is imposed by inserting each particle’s Fourier transform N times (for a N-fold group) during reconstruction, once in each possible symmetry-related pose.
symmetry allows us to reduce the angles considered during alignment
It does, but cryoSPARC doesn’t implement this optimization, because branch and bound is so fast that other optimizations have been prioritized over reducing the search space. Other refinement packages do limit the search space via symmetry - you can tell because the orientation distributions become restricted to the angles that have actually been searched.
exactly what symmetry expansion is doing
Your description is correct, except that the images aren’t usually literally duplicated. We make duplicate metadata entries with different symmetry-related poses, but they can all point to the same physical image. The particles could be re-extracted, but then the “duplicate” images will actually be slightly different, since they should be centered on different subunits within the particle. (They could also be smaller than the original box used for the whole particle).
A symmetry-expanded reconstruction should indeed be in C1, but should also use a mask focused on one asymmetric unit (but perhaps including interfaces with other subunits).