  This paper continues the approach of Kostenko \& Thompson to calculating
quantum electrodynamic processes in the ultrastrong magnetic field near some
neutron stars, such as magnetars or merging binary neutron stars. Here we
consider electron-positron scattering, the Coulomb scattering of electrons and
positrons off ions, and relativistic $e^\pm$-ion bremsstrahlung. The evaluation
of differential and total cross sections simplifies considerably when the
magnetic 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. Accurate
results for differential and total cross sections are obtained by truncating
the sum over intermediate-state Landau levels and otherwise disregarding terms
inversely proportional to the magnetic field, which are complicated enough to
have inhibited previous attempts to calculate magnetic electron-positron
scattering and relativistic bremsstrahlung. A quantitative account is made of
the effects of Debye screening.
