Two-photon excitation of Xe atoms in a static gas cell was used to prepare the Xe(7p[3/2](2), 7p[5/2](2), and 6p’[3/2](2)) states in mixtures of Xe with rare gases, H-2(D-2), CO, Cl-2, HCl, CCl2F2, CCl4, SF6, NS, CF4,CH4, CH3F, and N2O at 300 K. The total quenching rate constants were measured, and product fluorescence spectra were used to assign reaction pathways. The total quenching constants for these Xe* Rydberg states by molecular reagents are very large, corresponding to cross sections of 200-1500 Angstrom(2). Qualitative models are introduced to discuss the quenching processes, which are mainly reactive quenching and excitation transfer. For reagents with very large electron affinities, ion-pair formation may be important. A correlation of the quenching cross section with the dipole moment of the reagent was observed. These three Xe* states have nearly the same energy (similar to 11 eV), but the Xe(7p) states nominally have the Xe+(P-2(3/2)) ion-core, whereas the Xe(6p’) states have the Xe+(P-2(1/2)) core. The XeCl(D) and XeF(D) states also have the Xe+(2P(1/2)) core, and the fraction of XeCl(D) and XeF(D), relative to XeCl(B,C) or XeF(B,C), formed by the reactions of Xe(6p’[3/2]2) atoms with halogen-containing reagents can be used to measure the degree of conservation of the Xe+(P-2(1/2)) core. The Xe(7p) and Xe(6p’) reactions actually gave nearly the same B and D distributions, with XeCl(B) and XeF(B) being favored, and the Xe+(P-2(1/2)) ion-core state is not conserved during the reactions of Xe(6p’) atoms. Two-photon excitation of the Xe(7p,6p’) states leads to intense amplified spontaneous emission (ASE) unless special feature are incorporated into the experimental design. This ASE emission can cause complications because other Xe* states are generated during the laser pulse. The measurements reported here are free from ASE, but some consequences of ASE for experiments with Xe(6p’ and 7p) excitation are summarized. The relative two-photon cross sections of the Xe(6p, 6p’, 7p) states also are discussed.