There is a webserver which serves dynamic JSP contents, but we wish to serve some PHP contents too.
Can you really install PHP 5 and MySQL on Apache Tomcat 6..32 WITHOUT preventing the service of current contents, removing Tomcat, setting up the Apache HTTP Server (via AppServ, XAMPP or something like that similar which installs PHP, MySQL and phpMyAdmin too with only some simple clicks), and then, setting up the Apache Tomcat Connector?

Presently I not have the chance to configure the pointed out "target" webserver, however i installed Tomcat on my small local machine, so with my very own webserver I'm able to try doing anything recommended.

I understand you will find plenty of questions associated with the subject even on stackoverflow, but not one of them clarified my question.

Thanks ahead of time!

You could utilize Quercus or JSR223 + PHP-bridge to seeOrparse/run PHP files using Java.

Regarding MySQL, to be only a easy and stand alone DB server, it does not need a specific webserver. MySQL totally does not care wat webserver you are running. Just install and configure it the typical way.

Oh, please be aware the Apache Tomcat Connector requires Apache HTTPD server. Therefore if you won't want to install Apache HTTPD, then your Tomcat Connector is useless for you.

Tomcat supports CGI so why wouldn't you install php5-cgi?

I'm not sure whether you can install Apache Tomcat without HTTPD, however i can answer your question partly:

Automatically, it isn't possible. I'm not sure why, but package-contractors (I made use of Yummy at EC2) need you to install HTTPD too like a dependency of PHP. Therefore if your package-installer requires that as well, you have to build PHP from source (which is not very difficult though). Edit: I am using FastCGI, 'just' PHP may not work, however it would surprise me though. (FastCGI works since, much like MySQL, you are able to install PHP-FastCGI on the separate server).

MySQL is fully independant. Since also do the installation on the separate server (db-server) without PHP along with a HTTP-server, you can install MySQL without HTTPD.