  We extend our previous study of Hopf-algebraic $\kappa$-deformations of all
inhomogeneous orthogonal Lie algebras ${\rm iso}(g)$ as written in a tensorial
and unified form. Such deformations are determined by a vector $\tau$ which for
Lorentzian signature can be taken time-, light- or space-like. We focus on some
mathematical aspects related to this subject. Firstly, we describe real forms
with connection to the metric's signatures and their compatibility with the
reality condition for the corresponding $\kappa$-Minkowski (Hopf) module
algebras. Secondly, $h$-adic vs $q$-analog (polynomial) versions of deformed
algebras including specialization of the formal deformation parameter $\kappa$
to some numerical value are considered. In the latter the general covariance is
lost and one deals with an orthogonal decomposition. The last topic treated in
this paper concerns twisted extensions of $\kappa$-deformations as well as the
description of resulting noncommutative spacetime algebras in terms of solvable
Lie algebras. We found that if the type of the algebra does not depend on
deformation parameters then specialization is possible.
