We present a sample of 135,873 RR Lyrae stars (RRLs) with precise photometric metallicity and distance estimates from our newly calibrated P-{Phi}_31_-R_21_-[Fe/H]/P-R_21_-[Fe/H] and G-band absolute magnitude-metallicity relations. The P-{Phi}_31_-R_21_-[Fe/H] and P-R_21_-[Fe/H] relations for type RRab and type RRc stars are obtained from nearly 2700 Gaia-identified RRLs, with precise {Phi}_31_ and R_21_ measurements from light curves and metallicity estimates from spectroscopy. Using a few hundreds of nearby RRLs, with accurate distances estimated from the parallax measurements in Gaia Early Data Release 3, new G-band absolute magnitude-metallicity relations and near-IR period-absolute magnitude-metallicity relations are constructed. External checks, using other high-resolution spectroscopic samples of field RRLs and RRL members of globular clusters, show that the typical uncertainties in our photometric metallicity estimates are about 0.24 and 0.16dex for type RRab and type RRc stars, respectively, without significant systematic bias with respect to the high-resolution spectroscopic metallicity measurements. The accuracies of these metallicity estimates are much improved, especially for type RRab stars, when compared to those provided by Gaia Data Release 3. Validations of our distance estimates, again using members of globular clusters, show that the typical distance errors are only 3%-4%. The distance moduli {mu}_0_=18.503+/-0.001(stat)+/-0.040(syst)mag for the Large Magellanic Cloud (LMC) and {mu}_0_=19.030+/-0.003(stat)+/-0.043(syst)mag for the Small Magellanic Cloud (SMC) are estimated from our type RRab star sample and are in excellent agreement with previous measurements. The mean metallicities of the LMC and SMC derived in this work are also consistent with previous determinations. Using our sample, a steep metallicity gradient of -0.024+/-0.001dex/kpc is found for the LMC, while a negligible metallicity gradient is obtained for the SMC.