The CHandra Extended Emission Line Region Survey (CHEERS) is an X-ray study of nearby active galactic nuclei (AGN) designed to take full advantage of Chandra's unique angular resolution by spatially resolving feedback signatures and effects. In the second paper of a series on CHEERS target NGC 3393, we examine deep high-resolution Chandra images and compare them with Hubble narrow line images of [O III], [S II] and H$α$, as well as previously-unpublished mid-ultraviolet (MUV) images. We find evidence for a complex multi-phase structure in the circumnuclear ISM, with no single simple correlation between X-rays and high-ionization ([O III]/H$α$-dominated) and low-ionization ([S II]-dominated) features. We also find X-ray structures ~50-pc in extent, H$α$ evidence for gas compression, and extended MUV emission associated with the S-shaped arms that envelope the radio jets. In conjunction with existing STIS kinematics, these findings support a role for shock contributions to the feedback, driven by the radio outflows associated with the radio jets. ; Comment: Submitted to ApJ. Second paper in a series (after https://arxiv.org/abs/1604.02065). 32 pages, 21 figures. 63 eps files in the journal-submitted version have been converted to jpg here, due to arXiv submission size limit