Downloading a video should be “fair use” as recording a song from the radio

In Sony v. Universal, the usage of the VCR was justified based on a very narrow, very uncommon use case: if there were a TV show that aired exactly once, and for some reason you wanted to see it but couldn't, and it would never air again, you had the legal right to record one copy for later viewing. (I'm not sure if you had to destroy the copy after viewing it.) On that basis, and that basis alone, was the VCR ruled to have a legal use case. Otherwise it was pretty much a copyright violation device. Justice Blackmun, in his dissent, was clear that even making a single copy for personal use violates copyright law.

Fair use covers making excerpts of a work, not copying a full work, for purposes of reporting, criticism, parody, and the like. If you record or download a full song or video without permission, YOU ARE INFRINGING ON COPYRIGHT.

No. "Effective" is defined in section 1201 as meaning that the technological measure prevents copying "during the normal course of its operation" -- i.e., the "happy path" of the code prevents unauthorized copying. No matter how trivially the code may be broken, breaking it is a felony. A simple bit of JavaScript embedded in a page that prevents right clicks (to download images) would be an "effective technological measure" under the DMCA. If you put up a web page showing how to get around this with Chrome developer tools, you are "trafficking in circumvention tools" and can be found civilly/criminally liable under the DMCA.

Note that there are Library of Congress exceptions for circumventing, but not for trafficking. So you can figure out how to, say, rip DVDs yourself if doing so falls under a LoC exemption. But if you then turn around and publish how to do it, you are still in violation of the DMCA.