This thesis explores the conditions under which topological and other exotic superconducting phases may develop and their relationships to disorder and transmission modes in mesoscopic systems, where quantum coherence effects are relevant. First, building on Ginzburg-Landau effective field theory and a London equations phenomenological model for spatially inhomogeneous superconductors with anisotropic order parameters, I discuss experimental resolution limits for scanning superconducting quantum interference device (SQUID) susceptometry applied to superconductors exhibiting spatial structure on the scale of the coherence length. Resolution limits in the presence of structural disorder are quantified with theoretical analysis and experimental susceptometry measurements on controlled, nanofabricated hole array structures in niobium films. I discuss potential applications to experimental studies of electronic phase separation and structural disorder in unconventional superconductors and strongly correlated electron systems. Next, I discuss local susceptibility measurements on few-quintuple layer ternary 3D topological insulator (TI) bismuth selenide superconductor bilayers with niobium films. These measurements are motivated by predictions of pairing between helical Dirac carriers in the two-dimensional surface electron gas that lead to emergent properties such as supersymmetry and Majorana quasiparticles. We observe both local suppression and enhancement of diamagnetic susceptibility and critical temperature, which is consistent with structural and lattice disorder in the superconducting films. I discuss several implications for experimental susceptibility measurements of 3D TI NS bilayers using numerical solutions to semiclassical Usadel differential equations in the dirty-limit for superconductor-normal bilayers based on the Eilenberger-Larkin-Ovchinikov approximation. The final part of this dissertation discusses recent measurements of current-phase relations in SNS Josephson junctions on graphene-hBN Van der Waals heterostructures in finite magnetic fields, where we have observed anomalous phase shifts in the current-phase relations near the Dirac point. At the time of this writing, these effects are still not well understood. Our observations appear to be consistent with $\varphi_0$-junction behavior, recently observed in semiconductor quantum dot systems with large spin-orbit coupling, which is indicative of time-reversal and chiral symmetry breaking effects. Qualitatively similar phase shifts have also been observed in magnetoconductance measurements on these devices in the quantum Hall regime by our collaborators, but at much higher magnetic fields ($B> 1$ T). In our measurements at lower fields, this suggests that mixing between electron and hole modes may occur through delocalized states in the ballistic junctions, rather than strictly through scattering in quantum Hall edge states. Broadly, the results presented in this work hopefully will provide a basis for advancing future theoretical and experimental work towards understanding the interplay between topological phases and superconductivity in engineered quantum nanostructures and quantum materials.