Aims: For the first time accurate pulsation properties of the ancient variable stars of the Fornax dwarf spheroidal galaxy (dSph) are discussed in the broad context of galaxy formation and evolution. Methods: Homogeneous multi-band BVI optical photometry of spanning twenty years has allowed us to identify and characterize more than 1400 RR Lyrae stars (RRLs) in this galaxy. Results: Roughly 70% are new discoveries. We investigate the period-amplitude distribution and find that Fornax shows a lack of high amplitude (AV &ga; 0.75 mag) short period fundamental-mode RRLs (P ≲ 0.48 d, HASPs). These objects occur in stellar populations more metal-rich than [Fe/H] -1.5 and they are common in the Galactic halo (hereafter Halo) and in globulars. This evidence suggests that old Fornax stars (older than 10 Gyr) are relatively metal poor. A detailed statistical analysis of the role of the present-day Fornax dSph in reproducing the Halo period distribution shows that it can only account for up to 20% of the Halo when combined with RRLs in massive dwarf galaxies (Sagittarius dSph, Large Magellanic Cloud). This finding indicates that Fornax-like systems played a smaller role than massive dwarfs in building up the Halo. Conclusions: We also discuss the occurrence of HASPs in connection with the luminosity and the early chemical composition of nearby dwarf galaxies. We find that, independently of their individual star formation histories, bright (MV ≲ -13.5 mag) galaxies have HASPs, whereas faint ones (MV &ga; -11 mag) do not. Interestingly enough, Fornax belongs to a luminosity range (-11 < MV ≲ -13.5 mag) in which the occurrence of HASPs appears to be correlated with the early star formation and chemical enrichment of the host galaxy.