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In this study, we simulate mechanically interlocked semiflexible ring polymers inspired by the minicircles of kinetoplast DNA (kDNA) networks. Using coarse-grained molecular dynamics simulations, we investigate the impact of molecular topological linkage and nanoconfinement on the conformational properties of two- and three-ring polymer systems in varying solvent qualities. Under good-quality solvents, for two-ring systems, a higher number of crossing points lead to a more internally constrained structure, reducing their mean radius of gyration. In contrast, three-ring systems, which all had the same crossing number, exhibited more similar sizes. In unfavorable solvents, structures collapse, forming compact configurations with increased contacts. The morphological diversity of structures primarily arises from topological linkage rather than the number of rings. In three-ring systems with different topological conformations, structural uniformity varies based on link types. Extreme confinement induces isotropic and extended conformations for catenated polymers, aligning with experimental results for kDNA networks and influencing the crossing number and overall shape. Finally, the flat-to-collapse transition in extreme confinement occurs earlier (at relatively better solvent conditions) compared to non-confined systems. This study offers valuable insights into the conformational behavior of mechanically interlocked ring polymers, highlighting challenges in extrapolating single-molecule analyses to larger networks such as kDNA.