Confinement of cholesteric liquid crystals (ChLC) into droplets leads to a delicate interplay between elasticity, chirality, and surface energy. In this work, we rely on a combination of theory and experiments to understand the rich morphological behavior that arises from that balance. More specifically, a systematic study of micrometer-sized ChLC droplets is presented as a function of chirality and surface energy (or anchoring). With increasing chirality, a continuous transition is observed from a twisted bipolar structure to a radial spherical structure, all within a narrow range of chirality. During such a transition, a bent structure is predicted by simulations and confirmed by experimental observations. Simulations are also able to capture the dynamics of the quenching process observed in experiments. Consistent with published work, it is found that nanoparticles are attracted to defect regions on the surface of the droplets. For weak anchoring conditions at the nanoparticle surface, ChLC droplets adopt a morphology similar to that of the equilibrium helical phase observed for ChLCs in the bulk. As the anchoring strength increases, a planar bipolar structure arises, followed by a morphological transition to a bent structure. The influence of chirality and surface interactions are discussed in the context of the potential use of ChLC droplets as stimuli-responsive materials for reporting molecular adsorbates.