How do bands manage to perform around the world…and do the lyrics still rhyme and basically remain unchanged? I think about British or USA bands performing in Germany or Japan, as two examples. How is it done? Or, do they simply sing in English?
Guess what - your second option. There are some exceptions, but >99% of the USA/UK bands simply sing in English abroad.
I figured listening to songs in a language you can’t understand would be pointless - so why are all these Western bands popular in foreign countries? But then I heard Shakira singing in Spanish, which I can’t understand. And it’s infinitely better than listening to her sing English. Sounds more exotic… with an x, not an r. Mmmm, Shakira.
The Beatles converted a few of their earlier songs to German, quite possibly because they played in Germany a lot. But they were still popular even when they only sang in English.
Most bands these days stick to their languages, regardless of location. You don’t have to speak the language to like the song. For example, when I started listening to Einstürzende Neubauten, my German went only so far as guten Tag. I just liked how they sounded and had a vague idea of what they were singing about. I suspect that’s the case with a lot of people who attend concerts of a band from another country–they sound cool.
Don’t forget Peter Gabriels’ Deutsches Album! He sings it all in German, the version of “The Family and the Fishing Net” is particularly good.
Going in the other direction, how about Nena’s Neunundneunzig Luftballons"?
I think ABBA made a few tracks in other languages , especially Spanish. I agree that the the best versions by most artists are the ones in the original language. I am a great fan of Edith Piaf. She did record some songs in English but the French versions are so , so much better even though I cannot understand the words. The general “feel” of the song is that much better.
I guess that Bjork’s first band the Sugarcubes pissed off a few people at a New York performance where they sang the set in Icelandic. I personally would have enjoyed that.
When I travelled abroad I purchased dance music sung in Dutch, German, and French. It made for some great times when I slipped it into a few rave sets. People could not figure out if they were too messed up to understand it or if it actually was in a non-English language.
Years ago I bought an 8-track at a garage sale. It had a label made with a “tape tool” which stamped out Hebrew characters. I listened to the music; it seemed to be in Italian–or rather a Jewish dialect which is to Italian what Yiddish is to German and Ladino is to Spanish. One song I remember–and recorded onto an audiocassette–was apparently titled “Roberta,” which moved me because of a girl in high school with that name, whom I had insulted and still remembered. But that’s another story… 
I was never able to identify the singer or understand the Italian lyrics.
You’re overlooking one of the most classic releases of all time:
TOY SOLDIERS by Martika.
She released this instant classic not only in Spanish but also in Japanese…
<SARCASM off>
Anyway, I do think that there are songs that are good enough, so they become hits regardless of whether the audience actually understand the lyrics or not. I personally am I great fan of Mylene Farmer, but I don’t understand a word of French. Further, as a previous poster noted, Shakira’s songs in Spanish sound better than her songs in English.
Abba did some tracks in Spanish as mentioned. Roxette have released whole albums in Spanish due to the fact that they are huge in South America 
Huh? A great many of us foreign people understand English just fine, thank you. In fact, there are many Finnish bands which perform in English instead of Finnish (and one folk-black-metal band which performs in Swedish).