Question: Does PHP have global variables that can be modified by one running script and read by another?

Answer: 
Not as such, but you can use cookies or sessions to maintain data for duration of a user's browsing experience, or you can write to a database or file on-disk if the information needs to persist beyond that.
Global variables are bad in most programming. They're especially bad in multithreaded/multiuser systems like webapps. Avoid. If you must use global variables (rather than global constants) put them in a database with transactions guarding updates.

Since you talk about different scripts though, it sounds like what you really want is a web application framework in a more application oriented language --- something like Django (python) or Rails (ruby). These let you think of your code much more like a cohesive PROGRAM, rather than a lot of loosely connected scripts that process web requests.