LR 3 does work with XP if you have all the updates. I run it on both an XP and a Win 7 machine here and it's actually faster on the XP machine.
Lightroom is a major part of my work flow for image management and RAW processing, but it doesn't take the place of Photoshop. If you can only get one piece of software, get Photoshop Elements. Adobe Camera RAW in Photoshop has the same tools for RAW processing that Lightroom does. You don't get the file management, as previously mentioned, but IMO the editing tools take precedence.
Edited to add... the question about video editing... you can cut, splice, copy, paste, make a slide show, change audio, add simple effects... etc. In Premiere Elements. Adobe has 30 day free trials on their website if you want to check it out.