Create your own form

I know there are plug-ins available for creating your own contact form, but I’ve already made one for another site that I’d like to use.
How do I go about creating a page (with all its PHP code) without creating a ‘page’ within WP but still able to access WP includes?
I’d also like it to have the same sub-directory URL as other WP pages (e.g. mysite.com/this-directory/ ). WP pages’ URLs are created by mod-rewrite; can I have my custom-made page in that directory outside of WP?
And lastly, I’ve got a couple of pages on my site that are there on my site (I can see them) but when I go to validate the HTML, the W3C validator gives me a 404 error. Anyone else had something like this?