A time-dependent amplitude analysis of B0 → K0 Sπ+π− decays is performed in order to extract the CP violation parameters of f0(980)K0 S and ρ0(770)K0 S and direct CP asymmetries of K∗+(892)π−. The results are obtained from the final BABAR data sample of (465 ± 5)106 BB decays, collected with the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC. The time dependent CP asymmetry for f0(980)K0 S and ρ0(770)K0 S are measured to be S(f0(980)K0S) = −0.97±0.09±0.01±0.01, and S(ρ0(770)K0S) = 0.67±0.20± 0.06 ± 0.04, respectively. In decays to K∗+(892)π− the direct CP asymmetry is found to be ACP (K∗±(892)π∓) = −0.18 ± 0.10 ± 0.04 ± 0.00. The relative phases between B0 → K∗+(892)π− and B0 → K∗−(892)π+, relevant for the extraction of the unitarity triangle angle γ, is measured to be φ(K∗(892)π) = (34.9 ± 23.1 ± 7.5 ± 4.7)◦, where uncertainties are statistical, systematic and model-dependent, respectively. Fit fractions, direct CP asymemtries and the relative phases of different other resonant modes have also been measured. A new method for extracting longitudinal shower development information from longitudinally unsegmented calorimeters is also presented. This method has been implemented as a part of the BABAR final particle identification algorithm. A significant improvement in low momenta muon identification at BABAR is obtained.