  Motivated by the insulating behavior of $\alpha$-(BEDT-TSeF)$_2$I$_3$ at low
temperatures ($T$'s), we first performed first-principles calculations based on
the crystal structural data at 30 K under ambient pressure, and we constructed
a two-dimensional effective model using maximally localized Wannier functions.
As possible causes of the insulating behavior, we studied the effects of the
on-site Coulomb interaction $U$ and spin-orbit interaction (SOI) by
investigating the electronic state and the transport coefficient using the
Hartree approximation and the $T$-matrix approximation. The calculations at a
finite $T$ demonstrated that a spin-ordered massive Dirac electron (SMD)
appeared due to the on-site Coulomb interaction. We had an interest in the
anomalous competitive effect with $U$ and SOI when the SMD phase is present in
$\alpha$-(BETS)$_2$I$_3$, and we investigated these contributions to the
electronic state and conductivity. The SMD is not a conventional spin order,
but it exhibits the spin-valley Hall effect. Direct current resistivity in the
presence of a spin order gap increased divergently and exhibited negative
magnetoresistance in the low $T$ region with decreasing $T$. The charge density
hardly changed below and above the $T$ at which this insulating behavior
appeared. However, when considering the SOI alone, the state changed to a
topological insulator phase, and the electrical resistivity is saturated by
edge conduction at quite low $T$. When considering both the SMD and the SOI,
the spin order gap was suppressed by the SOI, and gaps with different sizes
opened in the left and right Dirac cones. This phase transition leads to
distinct changes in microwave conductivity, such as a discontinuous jump and a
peak structure.
