Youtube could easily copy that aspect of the DMCA and make it very expensive for mis-claimers, and easy to counteract automatic mis-classification. That they don't has nothing directly to do with laws, it's simply Youtube being a bad platform.
That simply is not true. DMCA misclaims are pretty much not punished at all in practice.
(However) I find it really difficult to believe the claimant in this case has no control over what YouTube does, as they have previously claimed. It may have been Content ID that got the identification wrong, but the claimant should not issue a block if it is a false claim.
Anyhow, Rousseau found a way around it by uploading a new version that received a copyright claim from a different company, instead of a block. He'll still have to go through the dispute process, at least we can watch the video because YouTube is not obliged to (and does not) take down the video.
No, it doesn't. There is only one part of a DMCA takedown notice that is made under penalty of perjury, and it's not the part that is usually at issue in a false notice.