I can declare the same variable in many files and they all points to the same symbol as far as the module is the same one. Right?

With the above correction, yes.

The only unfortunate exception is when you use threads. Then each thread inherits a cloned, non-shared copy of those globals already in existance in the thread from which it is cloned. If you want a shared global, you must post-fix it with :shared everywhere it is declared. Use it some places and omit it other and things get really messy.