  The neutrino and Higgs sectors in the $\mbox{SU(2)}_1 \times \mbox{SU(2)}_2
\times \mbox{U(1)}_Y $ model with lepton-flavor non-universality are discussed.
We show that active neutrinos can get Majorana masses from radiative
corrections, after adding only new singly charged Higgs bosons. The mechanism
for generation of neutrino masses is the same as in the Zee models. This also
gives a hint to solving the dark matter problem based on similar ways discussed
recently in many radiative neutrino mass models with dark matter. Except the
active neutrinos, the appearance of singly charged Higgs bosons and dark matter
does not affect significantly the physical spectrum of all particles in the
original model. We indicate this point by investigating the Higgs sector in
both cases before and after singly charged scalars are added into it. Many
interesting properties of physical Higgs bosons, which were not shown
previously, are explored. In particular, the mass matrices of charged and
CP-odd Higgs fields are proportional to the coefficient of triple Higgs
coupling $\mu$. The mass eigenstates and eigenvalues in the CP-even Higgs
sector are also presented. All couplings of the SM-like Higgs boson to normal
fermions and gauge bosons are different from the SM predictions by a factor
$c_h$, which must satisfy the recent global fit of experimental data, namely
$0.995<|c_h|<1$. We have analyzed a more general diagonalization of gauge boson
mass matrices, then we show that the ratio of the tangents of the $W-W'$ and
$Z-Z'$ mixing angles is exactly the cosine of the Weinberg angle, implying that
number of parameters is reduced by 1. Signals of new physics from decays of new
heavy fermions and Higgs bosons at LHC and constraints of their masses are also
discussed.
