I don’t know if they were ever heard in the original in the US or the UK, but two Russian songs made the charts:
“Dorogoi dlinnuyu” (aka “Those Were the Days, My Friend”) and “Podmoskovnye vechera” (aka “Midnight in Moscow”).
Does Australian count as ferrin? If so, men at work had a few.
Yes, pool-cue Sakamoto the rather lesser known brother of Ryuichi Sakamoto 
Yes, it is. Jamaican patois. Not a prestige dialect, and one that’s difficult to decipher for those unfamiliar with it, but English, nonetheless. (Snow copped an impressive Jamaican accent, considering he was born and raised in the Toronto area.)
[Edit - also? Reggae, not rap.]
Swahili. Something something jambo jambo (“hello hello”).
The non-English lyrics in All Night Long are made-up gibberish, only sounding like real words by accident (Jambo!, for one, is a Swahili greeting).
Actually, looking up the lyrics of Informer, it’s not even a particularly opaque example of patois. The accent he uses is worse than the wording. It’s a bit slow reading, if you’re not familiar with patois, but there’s little uniquely Jamaican vocabulary, and the story is pretty clear even with the eye-spelling and handful of completely dialectical words.
Funny, the top 40 stations in DC (Q107! and 105:WAVA!) only played the English versions back when it was big.
I was only nine or ten at the time, so I don’t really remember what got more play here. I definitely remember hearing the German version, as that’s my first clear memory of hearing German. My 4- and 2- year old daughters love that song, but unfortunately somehow ended up hearing the English version first, so these days I have to sit through that one. (Ok, they’re not that thematically different, though there are differences in the storyline, but something about the English version makes me cringe a little.)
Psycho Killer by the Talking Heads had a verse in French as well as a “Qu’est-ce que c’est ?” in the chorus.
Paul Simon’s Graceland had two tracks with non-English lyrics sung by Ladysmith Black Mambazo and charted on the album charts. Diamonds on the Soles of Her Shoes charted as a single in the UK; the other track, Homeless, doesn’t seem to have charted.
And just in case you haven’t seen it, here is Diamonds being performed on SNL before the album was released.
Blondie’s “Call Me” repeats the key phrase as "Appele Moi (French) and Chiama Me (Italian)
Lots of Jamaicans if you’re in the right parts of Toronto, and I think he grew up knowing Jamaicans.
They apparently thought it counted - “…Do you speaka my language? - He smiled, and handed me a Vegemite sandwich.” 
Good one, and a great performance. I’m embarrassed that I didn’t recall it right away. Simon caught a lot of shit for going to SA to record, because artists had boycotted doing performances in during Apartheid at the request of the ANC. In particular, Steve Van Zant was very vocal about condemning Simon, even though the ANC had approved his work there (providing he didn’t put on a concert, which would have been attended exclusively by whites), especially since he was hiring local talent at three times the pay normally handed out in the US. Other musicians recanted, but Van Zant never did.
When you read “Aah wuud wok fuive huundred muiles aand aaAah wuud wok fuive huundred moohre”, you might believe for a moment that it wasn’t English. 
Oh, he did, certainly - that’s how he got the name. But he was a teenager before he moved into that neighbourhood, IIRC, so I’m still impressed he picked up the accent to that extent (granted, only when he’s singing, but still).
Hah…you want something done in English by a British artist that sounds like it’s not English, try Shudehill by Shotty Horroh. I don’t know if Mancunian accents are always that impenetrable, but the sung bit (‘Drama, drama, what a palaver. Bless your mother, shame on your father.’) is the only bit I was able to actually understand without looking up the lyrics. (Not my type of music, but it was played a lot on a music station I watch over the last few weeks.)
Stretching, but Cobrastyle by the Teddybears is in Swedish, it hit #7 on the US Dance Club chart
We recently had a thread about “Sweet City Woman” by the Stampeders (#8 in 1971), which includes the deeply meaningful French lyrics