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This paper continues the approach of Kostenko \& Thompson to calculatingquantum electrodynamic processes in the ultrastrong magnetic field near someneutron stars, such as magnetars or merging binary neutron stars. Here weconsider electron-positron scattering, the Coulomb scattering of electrons andpositrons off ions, and relativistic $e^\pm$-ion bremsstrahlung. The evaluationof differential and total cross sections simplifies considerably when themagnetic field lies in the range $10^3B_{\rm Q} \gg B \gg B_{\rm Q}$, where$B_{\rm Q} \equiv m^2/e = 4.4\times 10^{13}$ G. Then, relativistic motion of$e^\pm$ is possible even when restricted to the lowest Landau state. Accurateresults for differential and total cross sections are obtained by truncatingthe sum over intermediate-state Landau levels and otherwise disregarding termsinversely proportional to the magnetic field, which are complicated enough tohave inhibited previous attempts to calculate magnetic electron-positronscattering and relativistic bremsstrahlung. A quantitative account is made ofthe effects of Debye screening.

QED Phenomena in an Ultrastrong Magnetic Field. II. Electron-Positron Scattering, $e^\pm$-Ion Scattering, and Relativistic Bremsstrahlung