You’re losing yourself… kernel logs won’t show you anything related with a web app. It’s dedicated to the kernel.
But if you really want to waste time on that, head to the /var/log/ directory (as root).
Otherwise, the logs that you’re looking for will be generated by the web server and not by the web app.
All the other questions are pure operating system questions and unrelated with a PHP web app (you won’t find much help here on that topic. AFAIK, we’re only a few SysOp here visiting this forum).
With that said, if you’re planning to make the app publicly available, I would highly recommend you to stay away from managing your own server. And go with a shared hosting where a qualified SysOp will take care of the operating system configuration.