  This is the second part of a work devoted to the study of linear Mahler
systems in several variables from the perspective of transcendence and
algebraic independence. From the lifting theorem obtained in the first part, we
first derive a general result, showing that Mahler functions in several
variables, associated with transformations having multiplicatively dependent
spectral radii, take algebraic independent values at algebraic points provided
that these points are sufficiently independent. Then, we focus on applications
of this result and of the two main results of Part I of this work. Our main
application concerns problems about the representation of natural and real
numbers in integer bases involving automata theory. These can be translated in
terms of algebraic relations over $\overline{\mathbb Q}$ between values of
Mahler functions in one variable. We also apply our results to the algebraic
independence of Mahler functions and their specializations, and to the study of
the values of Hecke-Mahler series.
