Are there are any security concerns when the read permission
is set on other i.e.; isn't it possible to write a program to
remotely read the contents of the file.
A bug in a server program listening over the network could allow this to happen (and it has happened before, even to Apache, if I remember correctly). Other than that, no, the web server would only serve the interpreted PHP scripts, not the PHP source code.
In this program I'll have the MySQL credentials defined.
However, if the web server does not invoke the PHP interpreter for some reason, the PHP source code will be served. Consequently, you should keep your database credentials in a file outside of the document root, so the web server will not serve it at all. You would then include this file in your relevant PHP script.
I am afraid I am not a security expert though, so for more information I have to refer you to the PHP manual's section on security.