I ran it in 35mm 6 or 7 years ago and it was a print sourced from the 1996 from the RAH restoration. Same for Rear Window. And while the print I ran of Man Who Knew Too Much wasn't touted as "restored", it also looked very nice.
Cary Grant appeared on radio dozens of times. Based on the content and sound of his voice, I'd guess it's from around 1940 or so. Certainly nothing to do with North by Northwest as that blog says it does.
The "Making of Vertigo" book says the composers of the Vertigo song were Livingston & Evans. I think that Internet page is mostly satire (really, The Beatles recorded a song written for The Birds? I don't think so...)
Indeed. I've had the pleasure of seeing an original release 35mm several times in the past 30 years (as well as running one once - very nervously!) and its always a treat.