I'll try to make sure I understand your question by restating it.
If you have a form (/form.php
), and the "action" of that submit button leads you to a separate php page (/form_action.php
), there is absolutely no difference in speed. Each HTTP request (form.php
and form_action.php
) is independent - "form_action.php" doesn't remember anything about "form.php" unless you pass that information through (as parameters). This is what people mean when they say that HTTP is stateless. It's worth learning about how HTTP works in general alongside the details of PHP.
If you have a PHP script which in turn includes other PHP scripts, there is a tiny performance impact - too small to measure in pretty much any case I've ever come across.
However, using includes allows you to separate your markup (the HTML) from the logic (the PHP). This is a really good thing if you are doing anything other than tinkering. It allows you to re-use functionality, it makes it much easier to change and maintain the code over time, and it helps you think through what you're trying to achieve.
There are many different ways people have solved the "how do I keep my code clean" puzzle; the current orthodoxy is "Model-View-Controller" (as @monty says). There are also PHP frameworks which make this a little easier to implement - once you've got the basics of the language, you might want to look at Zend or TinyMVC (there are several others, each with their benefits and drawbacks).