All of these assumptions are at least partially incorrect or, in the case of the last one, a bit nonsensical. You might want to find a good tutorial and also read through PHP The Right Way.
To address your assumptions in part:
1- A PHP script is launched when the file it resides on is requested via http.
Usually, but not necessarily. PHP files can also be run from the command line or via other protocols.
2- The script creates an independent scope for it's vars.
No. Any variables created outside of a function, class, or method have global scope and are automatically shared across any include
d or require
d files.
3- The script can only access any other DOM element at the end of it's execution. However, it can perform file's jobs any time.
This doesn't really make sense; PHP scripts don't have anything to with accessing the DOM. PHP runs purely on the server side. It can do anything on the server (assuming correct permissions, etc.) right up until it terminates.