Our aim in this paper is to investigate symmetry and reversibility pro-perties for quantum algebras and skew PBW extensions. Under certainconditions we prove that these properties transfer from a ring of coeffi-cients to a quantum algebra or skew PBW extension over this ring. In thisway we generalize several results established in the literature and consideralgebras which have not been studied before. We illustrate our results withremarkable examples of theoretical physics