The "second generation" fractional quantum Hall states containing a partially filled composite fermion (CF) Landau level (LL) are studied theoretically. The role of the unique form of the CF-CF interaction in the incompressibility of the underlying quantum electron liquid is explained. In particular, the two- and three-body CF correlation functions for these liquids are determined from exact diagonalization on a Haldane sphere. They are used to show that the CFs form a paired state (rather than a Laughlin liquid) when filling v = of their second LL. Similarly, at v = 1/2 the CFs do not appear to form a Moore-Read paired state but tend to group into larger clusters instead. The spin polarization of the interacting CFs is also investigated, and a transition to the partially unpolarized ground state is predicted in realistic conditions.