Solved by @[email protected], the song is "I Don't Want To Set The World On Fire" which is probably best known for the 1941 version by The Ink Spots that is used in Fallout games.
No, sorry. Fantastic song though, here's a hint: Both of our songs have more than three notable covers, though your song is far more impressive in both the amount of notable covers that have been released and the roster of talent covering the song.
Sorry, no. Here's a hint: the version of your song that is the most widely known is performed by the lead songwriter of the song; the songwriters of my song did not record any notable release but is instead well known through several popular covers, one arguably more than others.