We present an analysis of M31 RR Lyrae stars in six different fields using archival imaging from the Hubble Space Telescope. Published data for M31, M33, and several M31 dwarf spheroidal galaxies are also used to study the global properties of RR Lyrae in these systems. From the properties of RR Lyrae stars, we found that the majority of M31 and M33 RRLs are of Oosterhoff I (OoI),while those in M31 dSphs are of Oosterhoff intermediate. The main parameter affecting these Oosterhoff types is likely to be metallicity. Metallicity also plays a role in the lack of RRLs in the high amplitude short period(HASP, defined as those with P<=0.48 and A_V_>=0.75mag) variables in M31 dSphs. This difference in the properties of RRLs between their parent galaxy and satellites, as well as the lack of RRLs in the HASP region in dSphs can also be observed in the Milky Way (MW). Therefore, systems like these dSphs are unlikely to be the main building blocks of the M31 and MW halo.