Is it legal if I were to distribute a collection of various DVD movies, which I ripped on to my computer, shrunk and then fit on a DVD, and then gave that as a free gift in addition to an item in online auction that I have listed? Or would this violate some media distribution law?
You can't make copies of movies or music without the author's permission, except for personal backup purposes. It doesn't matter whether you're selling the copies or handing them out for free.
You could, instead, put a bunch of useful freeware programs onto a CD and hand that out. No law against that, and the authors don't mind. There is also other material out there that's in the public domain (i.e. old movies and classic literature that's over 75 years old), if you look hard enough.