We have determined integral and differential elastic cross sections for positron scattering with atomic F and F2 molecules from 0.01 to 1000 eV with different theoretical approaches. Higher order polarizabilities were successively considered in the scattering potential, and we observed that the differential and integral cross sections converge only when the pure dipole second hyperpolarization level is taken into account, demonstrating the importance of the hyperpolarization effects on the low energy positron scattering dynamics. Ramsauer structures were found for both targets, and in the particular case of the F atom, the effect of its quadrupole moment proved to be relevant around the position of the Ramsauer minimum, which was determined together with the scattering length for each of the adopted polarization schemes. A relation of these quantities with the matching radius between the correlation and polarization interactions is also discussed. Agreement between the model potential and ab initio cross sections for the lowest level of target polarization is found for F2. Since there is no previous theoretical or experimental determination of cross sections for these targets, we compared the differential cross sections of F2 with experimental data available for N2 and O2 and found reasonable agreement.