Can I play and analyze video files from DVDs, YouTube, or other web sites in Logger Pro?

This is a bit of a gray area. The short answer is "If you can play your video in QuickTime Player, you can also use it in Logger Pro."

The long answer is that it can be tricky to move video from one format to another. In some cases, the video is copyright-protected, and made intentionally difficult to transfer into a different format. Note that many video files are copyright-protected and attempting to break that protection may be illegal.

To download files from YouTube, there is a FireFox extension called "Video Download Helper", which is a free download from:
https://addons.mozilla.org/en-US/firefox/addon/3006

To get files from a DVD, there are several options which are often embroiled in legal battles. The most popular one is called HandBrake:
http://handbrake.fr/

Note that it may not rip all DVDs due to encryption.