Doppler free two photon absorption spectroscopy was employed to measure the pressure broadening and frequency shift rates of the 5S1/2 (F = 3) → 5D5/2 (F = 5, 4, 3, 2, 1) (778.105 nm) and the 5S1/2 (F = 2) → 7S1/2 (F = 2) (760.126 nm) two photon transitions in 85Rb by the noble gases and N2. To our knowledge, these rates are reported on for the first time. The self-broadening and shift rate of the 5S1/2 (F = 3) → 5D5/2 (F = 5, 4, 3, 2, 1) transition and self -broadening rate of the 5S1/2 (F = 2) → 7S1/2 (F = 2) transition were also measured. The temperature dependence of the self-frequency shift (Rb-Rb collisions) of these transitions is presented. Helium diffusion rates through Quartz and Pyrex cells are also calculated and the implication of helium diffusion through glass vapor cells is discussed in regards to atomic frequency standards based on these transitions. Experimental pressure broadening and shift rates are compared to theoretically calculated rates assuming a 6, 8 or 6, 8, 10 difference potential and pseudo potential model. Reasonable agreement is achieved between experimental and theoretical values.