We identified and characterized the largest (536) RR Lyrae (RRL) sample in a Milky Way dSph satellite (Sculptor) based on optical photometry data collected over $∼$24 years. The RRLs display a spread in V-magnitude ($∼$0.35 mag) which appears larger than photometric errors and the horizontal branch (HB) luminosity evolution of a mono-metallic population. Using several calibrations of two different reddening free and metal independent Period-Wesenheit relations we provide a new distance estimate $μ$=19.62 mag ($σ_{μ}$=0.04 mag) that agrees well with literature estimates. We constrained the metallicity distribution of the old population, using the $M_I$ Period-Luminosity relation, and we found that it ranges from -2.3 to -1.5 dex. The current estimate is narrower than suggested by low and intermediate spectroscopy of RGBs ($Δ$[Fe/H] $\le$ 1.5). We also investigated the HB morphology as a function of the galactocentric distance. The HB in the innermost regions is dominated by red HB stars and by RRLs, consistent with a more metal-rich population, while in the outermost regions it is dominated by blue HB stars and RRLs typical of a metal-poor population. Our results suggest that fast chemical evolution occurred in Sculptor, and that the radial gradients were in place at an early epoch. ; Comment: 10 pages, 5 figures, MNRAS accepted