No, wrong. The approval of that target of the parody (Amish, McDonalds, CIA etc) are not legally required.
Case law suggests that he is required to (and he does), license artist's music.
He's not parodying Miley Cyrus in 'Party in the CIA'. He's parodying the CIA. Because the lyrics and track aren't the subject, licensing of the track is required.
Similarly, If Repaer used a licensed font on the site, they'd have to license it.
I'm not sure about that. The definition of parody hinges on imitating an author or work (sometimes a whole genre), rather than on satirizing/critiquing subject matter unrelated to the author/work being imitated. He could write a song satirizing/critiquing the CIA and if it happens to imitate a song/style of Miley, then it's a parody of the latter, not of the former. Or a parody of nothing at all, in the strictest definition, since he's not satirizing/critiquing that which he's imitating.
When it comes to music copyright, certain aspects are copyrightable (therefore requiring license to use) and other aspects are not. Words and melody are (so Weird Al would need to license Miley's melody if he doesn't modify it sufficiently), but rhythm/chords/timbre/style/etc. are not (so Weird Al wouldn't need to license anything if he is merely copying those things from Miley). I think Al makes some songs with a copied melody requiring licensing, and some songs without that in which case no permission of any kind is legally necessary.
Right. Protected uses are protected because they were necessary. The Weird Al track that comes to mind which could be protected (but does not need the protection because Al always secures permission for these works) is "Smells Like Nirvana" because that specifically needs to use Nirvana's track "Smells Like Teen Spirit" because it's a (well meant, like a comedy roast) critique of Nirvana and their song. "It's hard to bargle nawdle zouss / With all these marbles in my mouth" is about Nirvana and about Smells Like Teen Spirit.
If you replace Smells Like Teen Spirit with Cliff Richards' "Saviours Day" it does not work, Cliff is not going to confuse and annoy your parents, his utterances aren't incomprehensible, and so on. The choice of song is necessary, which would justify protection.
Case law suggests that he is required to (and he does), license artist's music.
He's not parodying Miley Cyrus in 'Party in the CIA'. He's parodying the CIA. Because the lyrics and track aren't the subject, licensing of the track is required.
Similarly, If Repaer used a licensed font on the site, they'd have to license it.