Branching Fractions and CP Asymmetries in B⁰→ π⁰π⁰, B⁺→ π⁺π⁰, and B⁺→ K⁺π⁰ Decays and Isospin Analysis of the B → ππ System

Based on a sample of 227 x 10(6) BB pairs collected by the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC, we measure the branching fraction B(B0-->pi(0)pi(0))=(1.17+/-0.32+/-0.10)x10(-6), and the asymmetry Cpi(0)(pi(0))=-0.12+/-0.56+/-0.06. The B0-->pi(0)pi(0) signal has a significance of 5.0 sigma. We also measure B(B+-->pi(+)pi(0))=(5.8+/-0.6+/-0.4)x10(-6), B(B+-->K+pi(0))=(12.0+/-0.7+/-0.6)x10(-6), and the charge asymmetries Api(+)(pi(0))=-0.01+/-0.10+/-0.02 and AK+(pi(0))=0.06+/-0.06+/-0.01. Using isospin relations, we find an upper bound on the angle difference |alpha-alpha(eff)| of 35 degrees at the 90% C.L.