Is it possible, in my programs, to use variables I see in these source files?
Short answer: don't do it.
There's one thing that is called encapsulation. When you write a library, you design a "public" interface, i.e. a set of functions that a user of the library is supposed to call to perform whatever service your library provides. To achieve this, you might need some module-scoped(*) variables that can be accessed by the library code at your will without worrying about someone else tampering with them. If someone _does_ step in and modify those variable's value when he shouldn't, the library code might crash or produce wrong results.
Whatever you try to achieve by accessing a library-scoped variable via "extern" in your sketch is either doable by "properly" using the library or needs to be rethought.
(*) that is, variables that might be used by all functions in the library but that are not supposed to be visible outside it.