The PHENIX experiment at the BNL Relativistic Heavy Ion Collider (RHIC) has measured electrons with 0.3 < p(T) < 9 GeV/c at midrapidity (y < 0.35) from heavy-flavor (charm and bottom) decays in Au + Au collisions at root s(NN) = 200 GeV. The nuclear modification factor R-AA relative to p + p collisions shows a strong suppression in central Au + Au collisions, indicating substantial energy loss of heavy quarks in the medium produced at RHIC energies. A large azimuthal anisotropy v(2) with respect to the reaction plane is observed for 0.5 < p(T) < 5 GeV/c indicating substantial heavy-flavor elliptic flow. Both R-AA and v(2) show a p(T) dependence different from those of neutral pions. A comparison to transport models which simultaneously describe R-AA(p(T)) and v(2)(p(T)) suggests that the viscosity to entropy density ratio is close to the conjectured quantum lower bound, i.e., near a perfect fluid.