Remove namespace aliases from Core.h

We have some global namespace aliases in Core.h, which gets transitively included practically everywhere. This kind of defeats the purpose of the original namespaces. This issue is about removing the aliases and changing the code that uses them to introduce local aliases or use a sufficiently qualified name.

The implementation started out as moving implementation of a few functions from headers to namespaces, so my pull request will include those changes as well, unless someone objects.