is there any "in-use"-case for the specific PHP-file in AJAX?
For example: On my website there are numerous AJAX scripts running simultanious. The PHP script is already in use for a AJAX script. What does it mean for the other AJAX scripts? Do they connect to a new instance of the PHP script or what? Or am I completely wrong?
As @mudasobwa said PHP is (most of the times) stateless. It's not really PHP which is stateles, but it is HTTP which is a stateless protocol.
So that means every request is completely seperate from each other and they don't know anything about the request before or after. That's why there are things like SESSION, POST and GET to send or share information accross multiple PHP (HTTP) requests.
Also note this is the reason why you need to do things like authentication, database connection and query data every request.
As already mention in comments each request is separate.
However, if you are using sessions, in the php files requested by ajax, and the same request takes some time to process, your second ajax might hang, if this is trying to access the same session. This is due to the fact that php will lock your session file until it knows that the locking thread is done with it.
What you can do (if you are using session), is to close the session file by calling "session_write_close", when you know that you don't need to update the session.