In this chapter, the nonlinear dynamics and singularity of a crossing and product cubic system with a crossing-linear and self-quadratic product vector field are discussed, and the corresponding switching dynamics are discussed through the infinite equilibriums. A theory for the nonlinear dynamic behaviors of such a cubic system is presented through a theorem. Such a cubic system possesses parabola-saddles, third-order saddles, and centers. Parabola-saddles are the appearing bifurcations of saddles and centers. Third-order saddles are the appearing bifurcations from a saddle to a saddle, center, and saddle. A third-order source (sink) is the appearing bifurcation from a source (sink) to a source (sink), saddle, and source (sink). Up-down hyperbolic upper-to-lower saddles are the switching bifurcations of hyperbolic singular flows with a saddle and center. Parabola-saddles are the switching bifurcations of parabola-saddles with hyperbolic-to-hyperbolic-secant flows. Parabola-hyperbolic upper-to-lower saddles are the switching bifurcations of a third-order saddle and a hyperbolic-to-hyperbolic-secant flow. Parabola-circular upper-to-lower saddles are the switching bifurcations of a third-order center and a hyperbolic-secant-to-hyperbolic flow. Parabola-saddles on the inflection source and sink infinite equilibriums are the switching bifurcations of a saddle and a hyperbolic-secant flow with a center and hyperbolic flow.