I'd like to add a couple of static pages, using the same layout as in the forum (the one in search.php for example). Any idea on how to do that, without rebuilding the page myself?
You'd need to copy an existing page - like the search page for example.
Then you'd need to create a control file for your new page. Control files are named the same as their root page, but they sit in the /controls folder and contain all controls to be used on that page specifically.
So, the search page has search.php in the root, and it's control file is controls/search.php
Take a look at them and you'll see what I mean.
So, you can create a blank page by copying those and renaming them accordingly, and then remove / replace the search controls used on the search page with controls of your own.
If you don't "get it", it might help to read the order of execution document in the wiki: