In the last years, the NA48/2 experiment at the CERN SPS has recorded an unprecedented sample of charged kaon decays. From this, we report very precise measurements of fundamental parameters of Chiral Perturbation Theory (ChPT) and the study of low energy pi-pi scattering. Several rare and very rare decays have been studied. From more than 10^6 K+- -> pi+ pi0 gamma decays, a first measurement of the interference between Bremsstrahlung and Direct Emission amplitudes and a stringent limit on direct CP violation in this channel is presented. For K+- -> pi+ gamma gamma, about 1000 events have been selected, more than 30 times the existing statistics. Also, the first observation of K+- -> pi+ gamma e+ e- is reported with 120 events. For both decays, the branching fraction and the free parameter of O(p4) ChPT has been measured with high accuracy. Finally, we report on a new precise measurement of the branching fraction and form factors of K+- -> pi+- e+ e-, which is highly suppressed by the GIM mechanism. The measurement of the e+ e- spectrum is an important input for ChPT and probes the weak static interaction. The analyses of K+- -> pi+- pi0 pi0 (K3pi) and K+- -> pi+ pi- e+- nu (Ke4) decays give complementary approaches to the study of low energy pi-pi scattering. From data samples of ~90 Millions 3pi and ~1 Million Ke4 decays, precise values of a0 and a2, the Isospin 0 and 2 S-wave PI-PI scattering lengths, can be extracted with an unprecedented experimental precision, allowing accurate tests of Chiral Perturbation Theory predictions. The form factors of the Ke4 decays and their energy dependence are also measured with an improved precision, while the Dalitz plot parameters of the K3PI decays are determined including a new quadratic term.