Tomcat:
The short and simple answer is YES you can change an all HTML website to a PHP website. But you'd want to do it for the right reasons. If you only update the site every once in a while, and you're the only one that updates it, is it really necessary (or worth it) to redo it in PHP? Probably not. If you're a community site, and you have lots of contributors and you are not the only updater, it may.
The other thing to look at is how your site is constructed. Can you do a database driven site? In most cases one probably could, but it would take lots of work. Some easy ways in the beginning are using text-files and such. At least until you've got a handle on the true capacity of what SQL can do (and it can do A LOT, very very powerful).
As for just adding the PHP tags . . . it's a bit more involved than that. Yes, you could just add the tags, rename the file to *.php and WHAM! it's a PHP page. But that's not the true essence of PHP. If you're using it to serve up static pages, you can possibly be wasting valuable CPU cycles later on (with more visitors and more pages). If you have dynamic content (like a forum, blog, CMS, photo gallery, etc.) then it's best to use a server-side language to construct the pages and then serve it to the visitor.
The includes aren't really just a templating thing. They can be used for lots of things. Like separation of logic and configuration. You can have all your functions in one file, and then just include that function file. This is helpful for when you need to edit a function, you know where to find it: in the function file. Most PHP boards and pages use some type of external config file that is included at some point in time during the page generation process. But includes aren't limited to that. Also remember its sister function [man]require[/man] and the also useful [man]include_once[/man] and [man]require_once[/man] functions for only including/requiring certain files one time within a script (so as not to overwrite previous vars/code).
Databases are tables . . . so I'm not sure what you mean by "just for tables". Databases are for storage of information. You can store what you want from regular text to images to audio/video media. To store text you'd use the TEXT, SMALLTEXT, MEDTEXT, LONGTEXT field types. To store integers you'd use the INTEGER field types. But there are plenty of others. For the purposes of storing audio/video or images, you'd want to use the BLOB field. BLOB is the Binary Large OBject. It takes your "file" and reads its binary info, and stores it in there. Kinda cool. The downside is that it can really slow down your database when you get lots of media in there. It's best to store paths to files, and then store the files on your server (not in the database).
If you wanted to search through the text-file, you'd be better off just storing the text-file contents in a database table, and turning on full-text on that column. Then, when the user searches, search that column for their query. Much better than storing the actual text-file, or opening & closing many text-files.
My advice for a new person is to at least introduce yourself with the manual. It's an invaluable resource. A good tip is to install Firefox's PHP Search engine extension. You'll need it, and hopefully use it. Another tip is to get an editor that integrates the PHP manual, or one that has syntax checking. Two good ones are Zend Studio (boat load of money) or PHPDesigner 2006 (free from MPSoftware). Don't get stressed out over the smallest things/errors. Just take a deep breath, go away for an hour or so, come back and start working again. The hardest part about coding is getting everything right. It won't happen the first time, and practice makes perfect.
And to close out this long post, a quote (or two):
"Why do we fall Master Bruce?
So that we learn, to pick ourselves up"
~Alfred, Batman Begins (2005)
"Never Miss An Opportunity To Be Great"
~Friend of mine
