Wordpress is a very, very, VERY versatile tool. You cant do literally anything with it.
Its the easiest CMS around. (content managing system = lets you upload stuff to your site in a easy way)
joomla, drupal, nuke... all harder to code for than wordpress.
I suggest you find yourself a (free) domain and download Filezilla so you can connect with your site and upload Wordpress onto it!
About 7 months ago I started looking to get started with WP, took me a whole afternoon to figure things out, 3 hrs to find an instruction video! And another 3 to set it up. lol
Word press is pretty adaptable..
If you look at the code in the themes area you can see how it works ie.
there is a php file called comments.php, single.php for the single posts etc.
As for the theme there is no problems just modifying one of the themes to match your current website so it appears seamless as I have done at http://www.corporatehippies.com.au
You can then use the database information on any of your pages to display the output...
P.S I used wordpress for dummies the book, it's probably at google books to browse.
The result is basically a simple blog that doesn't look like a typical WP blog. I'm not a Wordpress expert, so I'm not sure this is the best way to do it, but but it's been working OK for a few months now.
I can't say I fully understand your problem, but this illustrates that you can fairly easily pull the data out of Wordpress without using WP templates.