I will try so that I understand your question by reformulating it.
If you have a form ( /form.php ), and the "action" of this submit button will lead you to a separate php page ( /form_action.php ), then there is no difference in speed. Each HTTP request ( form.php and form_action.php ) is independent - "form_action.php" remembers nothing about "form.php" if you do not pass this information through (as parameters). This is what people mean when they say that HTTP is stateless . It is worth learning about how HTTP generally works along with the details of PHP.
If you have a PHP script that, in turn, includes other PHP scripts, the tiny performance impact is too small to measure anyway anyway I have ever come across.
However, using include allows you to share markup (HTML) with logic (PHP). It is really good if you do something other than bother. This allows you to reuse functionality, it makes it much easier to change and maintain your code over time, and it helps you think through what you are trying to achieve.
There are many different ways people decide "how to keep my code clean"; current orthodoxy "Model-View-Controller" (as @monty says). There are also PHP frameworks that make this a little easier to implement - as soon as you learn the basics of the language, you can look at Zend or TinyMVC (there are several others, each of which has its advantages and disadvantages).
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