When either electron or hole doped at concentrations x approximately 0.1, the LaFeAsO family displays remarkably high temperature superconductivity with Tc up to 55 K. In the most energetically stable Q-->M=(pi,pi,0) antiferromagnetic (AFM) phase comprised of tetragonal-symmetry breaking alternating chains of aligned spins, there is a deep pseudogap in the Fe 3d states centered at the Fermi energy arising from light carriers (m* approximately 0.25-0.33), and very strong magnetophonon coupling is uncovered. Doping (of either sign) beyond x approximately 0.08 results in heavy carriers per Fe (by roughly an order of magnitude) with a large Fermi surface. Calculated Fe-Fe transverse exchange couplings Jij(R) reveal that exchange coupling is strongly dependent on both the AFM symmetry and on the Fe-As distance.