We study a potential hybrid quantum system with a plasmonic nanocavity coupled to a vibrating mode of single molecule and another optical cavity mode. To explore some important and valuable applications in quantum physics, we discuss and estimate several different applications with respect to the plasmon-mediated quantum interface, the plasmon-assisted engineering of two-mode continuous-variable entanglement, and pursuing an indirect and ultrastrong molecule-photon cooperativity. In addition, governed by the relation of symmetry breaking and quantum phase transitions (QPTs), the single-molecule induced QPTs is also studied in this tripartite hybrid quantum system. This theoretical study can strongly support the potential applications of this hybrid system in the field of quantum information processing (QIP). It is believed that our investigation on molecule-plasmon-photon hybridization can not only open a new avenue towards quantum manipulations, but also provide a fresh and reliable platform to carry out many applications with high efficiencies.