This is the last problem for now, I think. I see two undefined symbols in tropical.so. They are C++ symbols, which demangle to:
polymake::tropical::tropicalize(pm::Polynomial<pm::UniPolynomial<pm::Rational, pm::Rational>, int> const&)
polymake::tropical::pointlift(pm::Vector<pm::Rational> const&,
pm::Ring<pm::UniPolynomial<pm::Rational, pm::Rational>, int> const&)
I see that both are declared in apps/tropical/include/liftings.h, and are used in apps/tropical/src/points2hypersurface.c. But I don't see definitions for either.
Indeed, the definitions are located in a source file which has been precluded from exporting in the public distribution tarball by configuration. I've got to investigate by the authors whether they simply forgot to remove the blocking remark or still consider this code as not stable enough to be published. At any rate, the missing code will appear at the earliest in the next release; until then, please remove the files using the missing functions from your package.