Creating new files on the server
 

Let's say I want to create a new file via script on the server.
Is it done by fopen and fwrite?
How can the server prevent/allow this from happening?

Yes.
If the web daemon doesn't have write permissions to the directory, it should prevent it.

There are also shortcuts that generally amount to a wrapper for fopen, fwrite, and fclose. There are also functions for checking permissions. If you have a C/C++ background, be sure and read the documentation for the PHP version. Even those functions with identical names and purposes often operate a little differently. You might want to scan through the list of functions that you will find on this page and read up on the ones that capture your fancy. The PHP manual is really a very good resource.