Is there a mod, that allows you to show recent posts on a non vbulletin page?

You can do this without any hacks via javascript by utilizing the external.php?type=js

If you want to have recent posts via php on a non-vBulletin php based page, I'm pretty sure the hack already exists somewhere on www.vbulletin.org (99.99% positive, actually)

Should also be an RSS version of the recent posts, shouldn't there?

Yes, I would try vbulletin.org. I've been running one on one of my sites.