Can I include content from Pages in WordPress and output that content on any page outside of the WP install directory? Is there something specific I would need to include?
You can load WP engine in any PHP file, see integrating WP with your website in Codex.
Do I have to use a Theme or can I still use my already built CSS?
You can skip theme functionality completely, partially or you can create custom theme with your own CSS and code.
I’d like to be able to use my own CSS for the site and not have it be tied to a Theme – is that possible? Meaning I use www.example.com/css/styles.css vs www.example.com/wp-content/themes/styles.css.
Yes. Nothing prevents your from outputting arbitrary CSS in template over theme’s.
I also have a slider comprised of three DIVs for each panel, can I pull in that specific Page with that markup for the slider?
If you have sufficient understanding of PHP and learn some basic WP concepts – easily.
Can I also make my own queries for data as well?
Somewhat vague question. If you load WP engine you can use its API for database access. You can also query database directly but that would be much less secure and foolproof (especially if writing to it).
Is there anything that I won’t be able to accomplish or advise against doing?
Nothing you described so far seems extremely complex or impossible.
Overall, since from description the site is small and doesn’t have any special functionality, I’d consider just migrating it to WordPress completely.