We present improved measurements of CP-violation parameters in the decays B-0 -> pi(+)pi(-), B-0 -> K+pi(-), and B-0 -> pi(0)pi(0), and of the branching fractions for B-0 -> pi(0)pi(0) and B-0 -> K-0 pi(0). The results are obtained with the full data set collected at the Upsilon(4S) resonance by the BABAR experiment at the PEP-II asymmetric-energy B factory at the SLAC National Accelerator Laboratory, corresponding to (467 +/- 5) x 10(6) B (B) over bar pairs. We find the CP-violation parameter values and branching fractions: S pi+pi- = -0.68 +/- 0.10 +/- 0.03, C-pi+pi(-) = -0.25 +/- 0.08 +/- 0.02, A(K+pi-) = -0.107 +/- 0.016(-0.004)(+0.006), C pi(0)pi(0) = -0.43 +/- 0.26 +/- 0.05, B(B-0 -> pi(0)pi(0)) = (1.83 +/- 0.21 +/- 0.13) x 10(-6), B(B-0 -> pi(0)pi(0)) = (10.1 +/- 0.6 +/- 0.4) x 10(-6), where in each case, the first uncertainties are statistical and the second are systematic. We observe CP violation with a significance of 6.7 standard deviations for B-0 -> pi(+)pi(-) and 6.1 standard deviations for B-0 -> K+pi(-), including systematic uncertainties. Constraints on the unitarity triangle angle alpha are determined from the isospin relations among the B -> pi pi rates and asymmetries. Considering only the solution preferred by the Standard Model, we find alpha to be in the range [71 degrees,109 degrees] at the 68% confidence level.