In the presence of quenched disorder, the competition between local
magnetic-moment formation and Anderson localization for electrons at a
zero-temperature, metal-insulator transition (MIT) remains a long unresolved
problem. Here, we study the interplay of these ingredients in a power-law
random banded matrix model of spin-1/2 fermions with repulsive Hubbard
interactions. Focusing on the regime of weak interactions, we perform both
analytical field theory and numerical self-consistent Hartree-Fock numerical
calculations. We show that interference-mediated effects strongly enhance the
density of states and magnetic fluctuations upon approaching the MIT from the
metallic side. These are consistent with results due to Finkel'stein obtained
four decades ago. Our numerics further show that local moments nucleate from
typical states at the Fermi energy near the MIT, with a density that grows
continuously into the insulating phase. We identify spin-glass order in the
insulator by computing the overlap distribution between converged Hartree-Fock
mean-field moment profiles. Our results indicate that itinerant interference
effects can morph smoothly into moment formation and magnetic frustration
within a single model, revealing a common origin for these disparate phenomena.Comment: 21 pages, 18 figure