The hadronic form factors in the S- and P-wave and their variation with energy are obtained concurrently with the phase difference between the S- and P-wave states of the pi pi system. The latter measurement allows a precise determination of a00 and a02, the I=0 and I=2 S-wave pi pi scattering lengths. A combination of this result with another NA48/2 measurement, obtained in the study of K± →pi0 pi0 pi± decays, brings a further improved determination of a00 and the first precise experimental measurement of a02.  These measurements bring new inputs to low energy QCD calculations and are crucial tests of existing predictions from Chiral Perturbation Theory and lattice QCD calculations.