Let me answer from less 'technicall' point of view.
Apache is the HTTP server. It gets the HTTP requests and answers with the HTML code. PHP is used to generate this HTML dynamically on server side. MySQL is used by PHP for getting the data.
Once the Apache HTTP server gets the request for the page with php (or php3, php4, phtml or whatever is configured in Apache's config file), it calls PHP interpreter to generate HTML. Then this HTML is returned to the client - internet browser which sent HTTP request.
PHP has got an access to MySQL DB via several APIs. This simply means, that you can just call some function in PHP script to select, import update or delete some data in a table of DB. You can also maintain the DB, create, delete new tables a.s.o. There is a lot of functions for that ;)
Apache, MySQL, and PHP work together as a stack. Apache as the HTTP server, MySQL as the database, and PHP for scripting.
The best server yet for php serving is Apache, as PHP and Apache work closely together. The MySQL community database is a good server for PHP applications, this is why we talk about w/xamp servers, Windows/Linux Apache MySQL PHP servers.
No necessarily, PHP can be used on various other web servers, not just Apache, but Apache is the most popular. MySQL is a stand-alone database engine and is used by a lot of other stuff, not just PHP apps.
WAMP is an abbreviation of "Windows, Apache, MySQL, and PHP", so it uses MySQL database server.
*AMP (<OS> Apache Mysql PHP) stacks are incredibly popular, supported, and documented, creating a great environment for a beginner, and very much stable enough for a senior engineer.
WAMP stands for Windows Apache Mysql PHP. Mysql is the default database in WAMP
LAMP stands for Linux-Apache-MySQL-PHP. In simpler terms it contains everything to build a php application on a linux platform.
The main causes of errors in PHP can be the problems occurring from the MYSQL database (if there) or errors from Apache handler. These errors can be prevented by hosting the MYSQL database on a trusted and good server.
I know of 2. Mysql and OpenOffice.org. Mysql is very powerfull and easy to use along with PHP and the programming language running under apache. This will work in Windows, Linux and Mac OS.
facebook definatly runs on php (as you can tell by going to www.facebook.com/home.php). Also when you apply for a job to the company mysql knowledge is a must. However as for the platform it runs on that is difficult to say for sure, however i would imagine them to be using a classical LAMP setup (Linux Apache MySQL and PHP) as is very common with php/mySQL sites.
Both are Open-source and free. The combination of PHP and MySQL gives unmet options to create just about any kind of website - from small contact form to large corporate portal.
Ideal thing to do would be to delete all your installation & install a single WAMP/LAMP server. It combines all the features necessary to run php including windows/linux, apache, mysql & php
Apache server, database possibly mysql but other db's also work, ftp if it involves file uploads/downloads and last but not least a web browser to check the output from php code