Short version: No, no one has even been prosecuted.
Does the perjury clause apply to all the information in the notification, or only the statement that the complaining party is authorised to act etc. ?
This seems to be answerable by the plain text of the statute that you quoted:
A statement that the information in the notification is accurate, and under penalty of perjury, that the complaining party is authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.
There doesn't seem to be any remotely grammatical way to read "under penalty of perjury" as modifying anything in the first part of the sentence (i.e, the statement or the information in the notification). The closest we could come would be reading "A statement that the information in the notification is accurate, and under penalty of perjury" as saying that the information is both accurate and under penalty of perjury. Even if we ignore the fact that that would add a stray comma (as comma errors are not uncommon), that still leaves us with "that the complaining party is authorized to act on behalf of the owner of an exclusive right that is allegedly in-fringed" after an additional comma. This would need a conjunction (such as "and") that is not there in order for it to read at all correctly.
On the other hand, it is perfectly grammatical to read it as:
- that the information in the notification is accurate, and
- under penalty of perjury, that the complaining party is authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.
This would mean that only the statement that the complaining party is authorized to act on behalf of the copyright holder is made under penalty of perjury. Thus, the "statement that the complaining party has a good faith belief that use of the material in the manner complained of is not authorized" described in § 512(c)(3)(a)(v) and referenced in your second question is not made under penalty of perjury.
I couldn't find any case law regarding this, though, which brings us to the second question:
Has anyone ever actually been convicted of perjury as a result of sending a DMCA notice that lied about the "good faith belief" in the infringing nature of the target material?
As far as I can tell, no one has ever even been criminally prosecuted for sending false DMCA notices, let alone convicted. In fact, as far as I can tell, no one has ever been prosecuted for false copyright claims under any other laws, either. It's a bit difficult to find an authoritative reference stating something has never happened, and the best I found was the Wikipedia article on Copyfraud, which cites Fishman, Stephen. The Public Domain, Nolo (2006), pp. 24–29 for the proposition that (presumably as of 2006), "[n]o company has ever been prosecuted for violating" a related law on false claims of copyright. Obviously, that's not a great source, due to the date, not having access to the original text, and the fact that it's not quite the same law. I also tried quite a number of search terms on Google and found no criminal prosecutions there, either.
There have, however, been civil suits regarding such bad-faith misrepresentations: Automattic, owners of Wordpress.com, have filed at least two. In at least one of those, a lack of such a good-faith claim by the defendant was in fact found by the court:
Similarly, here, the Court finds that Defendant knowingly misrepresented that Hotham violated his copyright because Defendant could not have reasonably believed that the Press Release he sent to Hotham was protected under copyright. Moreover, there can be no dispute that Defendant knew, and indeed, specifically intended, that the takedown notice would result in the disabling of Hotham's article.
This resulted in the court finding the defendant liable for damages under § 512(f) for the time and money that the plaintiffs spent dealing with the results of the fraudulent DMCA takedown notice. Neither the court nor the plaintiffs mention perjury at any point other than quoting the takedown notice (unsurprising, though, given that it's a civil suit).