Travis CI used old cache and did not find the compilation
errors (instead it that errors has been found by us).
Also get rid of some Qt private parts, more fwd decls and so on.
Currently the build without implicitly included precompiled header
is not supported anyway (because Qt MOC source files do not include
stdafx.h, they include plain headers).
So when we decide to support building without implicitly included
precompiled headers we'll have to fix all the headers anyway.