We measure the branching fraction (B), polarization (f(L)), and CP asymmetry (A(CP)) of B(+/-)-->rho(+/-)rho(0) decays and search for the decay B(+/-)-->rho(+/-)f(0)(980) based on a data sample of 231.8 x 10(6) Upsilon(4S)-->BB decays collected with the BABAR detector at the SLAC PEP-II asymmetric-energy B factory. In B(+/-)-->rho(+/-)rho(0) decays we measure B=(16.8+/-2.2+/-2.3) x 10(-), f(L)=0.905+/-0.042(-0.027)(+0.023), and A(CP)=-0.12+/-0.13+/-0.10, and find an upper limit on the branching fraction of B(+/-)-->rho(+/-)f(0)(980)(-->pi(+)pi(-)) decays of 1.9 x 10(-6) at 90% confidence level.