A three-dimensional (3D) numerical experiment of the launching of a hot and fast coronal jet followed by several violent eruptions is analyzed in detail. These events are initiated through the emergence of a magnetic flux rope from the solar interior into a coronal hole. We explore the evolution of the emerging magnetically dominated plasma dome surmounted by a current sheet and the ensuing pattern of reconnection. A hot and fast coronal jet with inverted-Y shape is produced that shows properties comparable to those frequently observed with EUV and X-ray detectors. We analyze its 3D shape, its inhomogeneous internal structure, and its rise and decay phases, lasting for some 15-20 minutes each. Particular attention is devoted to the field line connectivities and the reconnection pattern. We also study the cool and high-density volume that appears to encircle the emerged dome. The decay of the jet is followed by a violent phase with a total of five eruptions. The first of them seems to follow the general pattern of tether-cutting reconnection in a sheared arcade, although modified by the field topology created by the preceding reconnection evolution. The two following eruptions take place near and above the strong-field concentrations at the surface. They show a twisted, Ω-loop-like rope expanding in height, with twist being turned into writhe, thus hinting at a kink instability (perhaps combined with a torus instability) as the cause of the eruption. The succession of a main jet ejection and a number of violent eruptions that resemble mini-CMEs and their physical properties suggest that this experiment may provide a model for the blowout jets recently proposed in the literature.